There's a point when I was reading the second half of Cheever's complete collection of stories (I completed first half earlier this year) when you think he can't better the one you've just read but he does.
For me he really raised his game consistently between the end of the 50s and early 60s. You could argue that this is the period when his alienated bourgeois suburban lifestyle was beginning perhaps to get a little dated in the States. Yet his laser like eye for detail means he really just hones his craft, outlining the destructive nature of these claustrophobic cocoons which the quite wealthy have put themselves into.
Unlike his Wapshot novels the sexual alienation which are felt by the characters (male mainly) is not represented by any gay encounters - with the slight exception of a couple of stories but through the constancy of adultery. The Country Husband (brilliant), the Chimera, the Brigadier and the Golf Widow all show the essential sadness of betrayal but also the essential sadness of the life which nominally they seem to want to escape from.
There are less classical references than his novels although one story Metamorphoses attempts to transfer Ovid's work to suburbia.
His later works also combine more Italian travels with the American world - some dealing with the ex pat world of the American living there - others with the Italian attempting to fit into modern consumer capitalism: Clemintina for example. I recently saw the Antonioni movie L'Avventura based in Sicily and the time frame (1960) and the group it focussed on - the Italian wealthy reminded me strongly of Cheever's work.
As the stories progress (this work is chronological) the early references to the servants and the poor of consumer post war America are less. The focus is more on the internal distintegration of these high salaried individuals with their world of hard liquor and regular trains. There are also very little specific historical points of reference although there is an excellent working in of a domestic nuclear bunker within suburbia in the Brigadier story- around the Cuban Missile crisis. He even creates his own suburban neighbourhood, Bullet Park - the title of one of his later novels.
The zenith I think comes with the Swimmer (written in 1967) - unsurprisinglythe basis of a movie with Burt Lancaster. It is breathtaking in what it does in such a short space - it's only around 10 pages yet Cheever considered making a novel on the theme , having 150 pages of notes. This condensing intrigues me and is really more like the mechanics of writing poetry. The work is quite experimental and every word is relevant and powerful. It concerns the travel of a man across his suburban landscape swimming through each of his neighbours' swimming pools - but embarking on the journey he (and Cheever) drill down to exactly what this society represents - the deceit, the social climbing- and exposes the whole edifice with a chilling final paragraph. It's like a summary of all of Cheever's work, quite brilliant.
An unfortunate theme in some of these later stories much more prominent than in his earlier work is the deceitful and selfish nature of women : Clementina, An Educated American Woman and The Geometry of Love leave a slightly bitter taste in the mouth over their portrayal of women. Not that men get it much easier it just seems a bit nastier - I think there was quite a lot of turmoil in his private life at this time which is definitely worked through here.
I would also add that the last few stories written in the 70s when he also wrote two novels are a little weaker perhaps because they don't have the discipline and tightness of the other prose which were published in the New Yorker magazine. Ironically they seem to come from the collection called the World of Apples - the titular story concerns an old highly respected poet (An American in Italy)who becomes focused on sexuality and obscenity as he nears the end of his life - writing endless dirty limericks until he resolves the issues. Yet all Cheever's subsequent stories are equally explicit with reference to orgies, pornography and masturbation - he apparently had to publish them in Playboy as the New Yorker refused. They don't really work for the most part although even them have the occasional phrase or sentence which reflect his brilliance as a writer.
So flaws exposed as his work and indeed his life drew to a close but an amazing collection of work. 2011 has been an eventful year but one of my highlights has been my discovery of John Cheever's writing.