Worlds of the Imperium by Laumer, Keith - 1967

"A parallel-time-tracks story with van Vogtian wheels-within-wheels ramifications. Brion Bayard, of our own continuum, is snatched into one in which there never was a United States, in which Northern Europe, Britain, the Western Hemisphere and Australia form one huge empire, in which Hermann Goering is a useful ally. He learns that there is still a third continuum, in which nuclear war has nearly shattered civilization, leaving a North African dictatorship headed by - himself.
"The scheme: replace the bad Brion Bayard with the good one and stop the guerrilla raids on the Imperium.
"Naturally Brion falls in with this plan, and naturally things are not quite as simple as they seem ... Well-done action, adventure and cloak-and-dagger stuff. " - P. Schuyler Miller (Analog) .