In Harry Turtledove's novel and the story In the Presence of Mine Enemies, the USA stays neutral and doesn't interfere in World War II. This means that Nazi Germany and the Japanese Empire systematically defeat their enemies and carve up the rest of the world. In the late 1960s or early 1970s, the two allies invade and conquer the U.S. and dominate the rest of the world. The Greater German Reich parallels certain points of the Soviet Union's OTL history at various points.
In the novel, Heinz Buckliger becomes the Führer of the Reich in 2010. His rise follows an arc similar to the rise of Mikhail Gorbachev in the OTL USSR. Both reached the high office by rising through their respective governments, working primarily through bureaucratic posts (Buckliger was Minister of Heavy Industry while Gorbachev was Head of Department of Party Organs). This rise represented something of a break with tradition in both countries, where strong party and/or military ties were important qualifications for the high office. Both were considerably younger when entering their office than most of their predecessors were. Both were quick to begin reforms while using the very conservative apparatus of their respective countries.
Both men face coups by the conservatives in their respective countries. Buckliger is put under house arrest in Croatia while Gorbachev was arrested for a time in Crimea. The fictional coup against Buckliger only lasts about a day before failing. The coup against Gorbachev lasted about three.
Finally, after both expanded democracy introduced into their countries, and planned to stay in power, both were overshadowed by more aggressive and populist leaders who'd publicly defied their countries' respective coups. As the novel ends shortly after the coup is suppressed, whether or not Buckliger met the same political fate as Gorbachev is unknown.
Turtledove does break from the Gorbachev parallel at one point by having Buckliger give a secret speech to Nazi leaders, largely condemning the oppressiveness of the Reich under past leaders. This is similar to a speech Nikita Khrushchev made on 25 February 1956 which was critical of Joseph Stalin.
Rolf Stolle is based on Boris Yeltsin, who succeeded Gorbachev as the first President of ex-Soviet Russia. For starters, both are depicted as something of buffoons (Heinrich Gimpel likened Stolle to Hermann Göring) at least in the point of view of the general public and are mayors of their respective countries' power centers. They also took great steps to portray themselves as a 'man of the people' and were popular with the people they governed.
Both were known for supporting reforms and indeed becoming leaders of the democratic movements. And, importantly, both were opponents of the coups that tried to bring down the democratically elected governments in their countries (although the 2011 coup of the SS happened before elections). There is a difference however. In the coup in Nazi Germany, the SS, the secret police service, were the ones who rebelled and the reformists were saved by the German Army. In OTL, the Soviet Red Army was the one who attempted to take power.
Notably during the Soviet coup against reforms, Yeltsin stood on a Red Army tank defying his opponents. In the novel, Stolle defiantly kicks an SS tank.
Kurt Haldweim is directly based on Austrian politician Kurt Waldheim, who served as President of Austria from 1986 to 1992. Before that, he served as the United Nations Secretary General from 1972 to 1981. Aside from the pun on their names, both evidently share the same birthday, both were born in Austria, and both served in military intelligence during World War II.
Haldweim has many aspects of Leonid Brezhnev. For instance, both had ruled their countries as long as the founders (Brezhnev ruled as long as Joseph Stalin while Haldweim ruled only a few years fewer than Adolf Hitler himself).
It was also in their respective tenures that their countries fell under economic stagnation.
The Führer's Palace
The Führer's Palace is based on the Russian Kremlin as the housing for the rulers of the country. They both have enormous squares in front of them (the Palace has the Adolf Hitler Platz in front of it as the Kremlin has the Red Square in front of it).
The Adolf Hitler Platz
The Platz is very similar to the Red Square in its size and splendor. Also, both places saw massive civil demonstration for democracy.
Parallel Plot Points
Hardliners Stage Coup...and Fail
In OTL, the conservatives in the Communist Party rebelled with the help of the Red Army, naming themselves the State Committee of the State of Emergency, with the aim of wiping out reforms that introduced democracy in the Soviet Union. In the Greater German Reich, the SS with help of Nazi Party conservatives, who together called themselves the State Committee for the Salvation of the Greater German Reich, launched a coup to try and stop democracy in the Reich.
Both coup attempts failed due to civilian demonstrations and which were aided by the military (in OTL, the Red Army's mutinous soldiers. In the story, by the Wehrmacht).
Victorious Reformists Allow Greater Autonomy in Occupied States
In OTL, after the Soviet Union held free elections, countries that had been ruled by Moscow began to secede and establish their own republics, leading to the dissolution of the USSR. In the novel, after the Reichstag elections, the Reich seems comfortable with granting increasing calls for autonomy in several (but not all) of their possessions.