Influence on and by the work of Ilf and Petrov

Their predecessors

It has often been stated that Ilf and Petrov wrote in the satirical tradition of Gogol and Saltykov-Shchedrin. This is true, of course, though it does not do justice to Gogol, who was much more than a satiricist. (And so, incidentally, were Ilf and Petrov, see elsewhere on this site. However, I think few will object that they were satiricists, more so than Gogol.)
If you want to learn more about the issue of influences on the work of Ilf and Petrov I advise you to read Shcheglov's magnificent Спутник. Two influences mentioned by Shcheglov which are less well-known than the above-mentioned writers are Ehrenburg - in particular his Julio Jurenito - and the Satirikon writers (especially Averchenko and Teffi), who were unmentionable during Soviet times, because they emigrated after the Revolution. Ilf and Petrov had certainly read their work and their influence is beyond doubt.

Their successors

This is another subject for which I would very much appreciate input by readers.
Ilf and Petrov wrote in a literary tradition. Which later writers continued this tradition?

I do not pretend to be an expert on world literature. Therefore I will discuss some Dutch writers here and appeal to the reader for input for other languages, including Russian.

Dutch
    - Elsschot
    - K. van het Reve
    - Van Kooten en De Bie

English
    - Nabokov

Dutch
Willem Elsschot (1882-1960) was one of the best Dutch writers of the 20th century. Some would call him a Flemish writer, but his Dutch was impeccable and hardly, if at all, recognizable as written by a Belgian. His first novel, Villa des Roses (1913) is already a completely mature masterpiece.
One of the things which he shares with Ilf and Petrov is that his prose loses much in translation. His style is sobre but very tense. It gives one the feeling of great 'inflammability', to paraphrase Karel van het Reve (see below).
I mention him here because of his novels Lijmen (1924, translated in English under the title of Soft Soap) and Het been ('The leg', 1938). The novels are told by Laarmans, a kind of alter ego of Elsschot himself. The other hero is a man called Boorman, who is in various respects similar to Ostap Bender. He is very intelligent and a bit aloof from society. He understands human nature very well and uses this ability to make money.
Central in these two novels is a magazine with the comically pretentious name Algemeen Wereldtijdschrift voor Financien, Handel, Nijverheid, Kunsten en Wetenschappen, of which Boorman is the director. He publishes very flattering articles about companies and then sells large quantities of copies to this company, which then is supposed to distribute it to its potential customers. The point is that the companies in their optimism and vanity tend to order far too many copies. Boorman's activities, like Bender's, are formally legal but border on crookery and sometimes contain an element of blackmail.
The Laarmans character resembles Vorobyanninov in some respects. He is less smart than Boorman and makes mistakes. Like Vorobyanninov he is sometimes ordered to keep silent during meetings and also his name is changed like Vorobyanninov's.
Lijmen ends with a very succesful transaction with a small elevator factory to which Boorman sells 100,000 copies of the magazine. The factory is the property of a married couple - the wife, a rather pitiful character with a sick leg, closes the transaction. When they realize that they absolutely do not need 100,000 copies, it is of course too late. In Het been remorse hits Boorman. The mega-transaction has not made him happy, like Bender's million does not make him happy in The Little Golden Calf, though for different reasons. Boorman now tries to buy back the copies, but the wife, driven by a stubborn feeling of honour, does not let him. Only at the very end he succeeds - the ending is happier than that of The Golden Calf.
Elsschot was interested in the Soviet-Union and like many other western intellectuals was optimistic and moderately positive about the developments in the country. As far as I know, however, he did not know Ilf and Petrov.

Drawing by Peter van Dongen

Karel van het Reve (1921-1999) is not primarily known as a novelist but as a publicist writing about diverse subjects, including literature, religion, Darwinism, Freud and many others. He is famous for his crystal-clear, elegant style, his erudition, humour and wit.
Son of a active communist, in his young years he firmly believed in the communist cause, but after the war he lost his 'faith' and became a very outspoken anti-communist, which he remained for the rest of his life. He studied Russian and wrote his PhD thesis on the esthetics of Soviet-Russian marxism. In 1968 he was correspondent in Moscow for the Dutch newspaper Het Parool. He wrote about dissidents like Belinkov and Amalrik and supported them. Van het Reve was the person who first brought Sakharov's Reflections on Progress, Peaceful Coexistence, and Intellectual Freedom, to the attention of the public. In 1957 he was appointed Professor of Slavistics in Leiden. He wrote a very interesting - if somewhat controversial - history of Russian literature up to Chekhov. Van het Reve wrote a lot about Russian literature, but his interest was mostly in the 19th century and in 20th century dissident writers.
There is however a rather curious mention of Ilf and Petrov in his Collected Works (my translation):
"It is very interesting to observe how readers who like a book get attached to the translation in which they happened to read it. When I was about sixteen years old, I read The Golden Calf by Ilf and Petrov in a Dutch translation by S. van Praag. It was called Een millionair in Sowjet-Rusland. I got so much attached to that text that I have never wished to read the Russian original. 'Gravin loopt krankzinnig van angst in vijver' [Графиня изменившмся лицом бежит пруду - PJ] is for me the original text [...]" (Van het Reve then proceeds to state that he understands that this is an inadequate translation.). This truly baffles me. He was Professor in Slavistics at the time but apparently did not think he simply had to read this book in Russian. Whereas when writing about English or German literature he always quoted in the orginal language.
Anyway, he definitely read and admired The Golden Calf. When after his death his library was auctioned to raise money for the publication of his Collected Works, I bought his copy of Как создавался Робинзон.
Besides his essayistic work Van het Reve wrote two novels. The second, Nacht op de kale berg ('Night on the bare mountain', 1961), is the one I want to discuss here. The two heroes, Joop Flavius and Bram van Heel, form another Bender/Vorobyanninov pair, though they may rather be inspired by Elsschot's Boorman and Laarmans, since Van het Reve admired Elsschot very much - this novel contains a few hidden references to Lijmen.
The plot of the novel has some striking similarities with The Golden Calf. The two heroes meet a very nice girl, who is just as attractive and morally stable as Zosya Sinitskaya. She is taking care of an elderly gentleman, whom 'she would not marry even for a million guilders'. "Would you marry one of us for a million?" Flavius asks. Well, she might consider it. They agree to meet again in exactly one year and the two friends set out to gather a million. Flavius concludes that the best way to earn a million on such a short term is 'to very urgently ask for it', so that it will be 'handed on a golden platter'. He organizes a religious sect (the novel is, among other things, an anti-religious satire), whose believers are supposed to contribute 10 percent of their income to the building of a Temple. (Dutch readers who consider reading the novel are advised to skip the next part, since I will reveal the plot.) After some adventures the friends really manage to gather a million. However, when they present the money to the girl, she is flabbergasted and says: "You should not have done that. I will not accept the money." After a short discussion she walks away.
And then they do what Ostap considered doing as well, but rejected as 'пижонство, гусарство': they burn the money. And then there is a marvellous, brilliant final twist at the end, which I will not go into here.
To me the similarities are striking, even though Van het Reve was following in the footsteps of Elsschot rather than Ilf and Petrov.

Finally I cannot help mentioning Van Kooten en De Bie here. They were a famous television duo, who presented satirical sketches on television for more than twenty years. Their satire was not unlike Ilf and Petrov's: sometimes with ambiguous irony, leaving the reader in doubt what their real view was. And most importantly, with a great feeling for language. Like Ilf and Petrov they made a great contribution to their native language, creating words and phrases which are still used, often without the user being aware of the origin.
Like Ilf and Petrov they were immensely popular, not only with the cultural elite but also with the 'general public'. And even young people, from after the television days of Van Kooten en De Bie, generally know their name and have seen some of their sketches.
They are both writers as well. Some of De Bie's short stories are very close to Ilf and Petrov's short stories in their tone, style and subject matter.
And they wrote together as well: between 1972 and 1986 they published a so-called 'Bescheurkalender' (a pun on scheuren, 'tearing off', and zich bescheuren, 'laughing out loud', i.e. a humorous block calender) every year. In 1986 a magnificent anthology of these calenders appeared: Het Groot Bescheurboek.
I have no information about their having read the work of Ilf and Petrov.

English

Sergey Gandlevsky suggests a relationship between Vladimir Nabokov and Ilf and Petrov. In an interesting article in the magazine Citata he first discusses general similarities between the works of Nabokov and those of Ilf and Petrov and then more in particular points to Lolita as being in a sense a more modern, American version of the Bender novels, with Humbert Humbert of course in the role of Bender, travelling the country and having to deal with its petty bourgeois inhabitants, just like Bender.
Personally, I think this is a bit far-fetched, although some similarities are certainly present. However, if Nabokov really had Bender in mind when creating Humbert Humbert, he would have built-in some obscure allusion or hint, and such an allusion has not been identified as far a I know.
Nabokov has alway rejected the idea of Lolita being a satirical novel about America: "Satire is a lesson, parody is a game," he used to say. He disdained filologists who approached Gogol only as a satiricist, and I am sure that, would he have teached about Ilf and Petrov, he would not have treated the satirical aspect of their novels very extensively. On the other hand, I think one cannot deny that Lolita does have some satirical elements.
To sum up, I do not think that Nabokov consciously hinted at Bender in his creation of Humbert Humbert, but I do think there is some relationship to be seen, and comparing Lolita and the Bender novels is a potentially useful exercise.
It is also interesting to compare the travels of Humbert Humbert and Nabokov in America with Ilf and Petrov's American roadtrip.
We know that Nabokov admired Ilf and Petrov. See for more information the Citata article mentioned above.