When Khrushchev was (peacefully) removed in 1964, a "minister without a portfolio" Mikhail Suslov proposed that there will be no single leaders and top decisions will be made by a committee. And so it became with Brezhnev as the top man (aka the General Secretary), Suslov as #2, Aleksey Kosygin as # 1.2 (a prime minister, the chairman of the council of ministers), the KGB head Vladimir Semichastny (removed by 1967 and replaced by Yuri Andropov as more susceptible to the Party ideas, being a CPCU careerist rather than a NKVD/KGB based careerist as Semichastny). In and out were other personalities such as the Prime Union leader Podgorny (he was an idiot and disliked), various Ministers of Defense (first old WWII era general Malinowski, not an ally with Semichastny), then an old Brezhnev crony Grechko, then after Crechko's passing a long time head of the military industry Dimitri Ustinov.
In 1975, Kosygin was dead for a month (he drowned while boating, his bodyguard literally fished him out).. A year later, Brezhnev had a stroke. That basically created a fight for the survival. There were two rival clans - the Dnipro clan (Brezhnev was from Dnipro in Ukraine), with Brezhnev, Suslov and any potential allies. They wanted a continuation of the existing regime. Their main opposition was the "Leningrad clan", with Kosygin (a prime minister and an ex-businessman during the free market NEP 1920's), Andropov and Ustinov. They wanted a switch similar change to what Deng Xiaoping accomplished in the Communist China. The soviet economy had two parts - international oil and gas sales. And disaster everywhere else. As the replicement for the aging regime, "the Leningrad clan" wanted the head of Belarus Peter Masherov, a highly charismatic 61-year old. In August of 1980, Macherov was murdered ( a car accident was staged) by Brezhnev's crony the head of the state police Nicolay Schelokov and assisted semi-directly by Brezhnev's own son-in-law, Schelokov's top deputy Yuri Churbanov. Andropov, who was despised by Schelokov, was also targeted but had top bodyguard groups working on his defense.
Kosygin died in October, 1980 and was replaced by s "neutral" Nicolai Tikhonov. Suslov died in March, 1982, Brezhnev himself died after the November holiday of 1982 and Andropov by then moved enough pieces forward to place himself as the head head. He removed Schelokov and Churbanov after coming to power. In 1982, Andropov died and he he knew he couldn't bring out his Plan B Michael Gorbachev forward. For a year, it was a de facto trio - the official general secretary was Konstantin Chernenko (but he was very sick by then), and Dmitri Ustinov with Andrey Gromyko being his co-ministers, with Gorbachev running the daily grind, whenever Chernenko couldn't make it out of bed. Chernenko and Ustinov died in 1984 and Chernenko got the top job. By then he moved the "new types" to Kremlin, having fired the old Brezhnev era leaders, Victor Grishin (head of Moscow, an a potential replacement) and Gregory Romanov (head of Leningrad and likewise)
For the record, the criminals in charge of the early 80.s. Yuri Churbanov on the left, Brezhnev's daughter, his wife Galina and the head of the state police Nicolay Scherbanov.
