C.build up his country's military power during the period of détente.
Brezhnev met with American presidents Nixon and Ford and signed nuclear arms limitations agreements with them. And also during the Nixon and Brezhnev years, the US and USSR participated in a joint mission in space, the Apollo-Soyuz Test Project.
But military buildup continued in great measure under Brezhnev -- from the Soviet view, to keep pace with American power. Defense spending increased 40% during Brezhnev's early years, from 1965 to 1970, and continued to increase annually thereafter. The "Brezhnev Doctrine" called for the Soviet Union to intervene anywhere that socialist government was threatened, so there were military deployments outside of the USSR, in places like Czechoslovakia and Afghanistan.