the yankees had their sattelites and their own military program - gemini I think .
Both sides planned for orbital fighters and bombers to combat spacestation and satelittes .The Russian side was eager to get a system up to combat the US spy satelittes .The Almaz station was tested with modified 30 mm and 23 mm autocannons against target drones.Making shootdowns ,the program was deemed possible but a variety of factors such as the development of treaties towards leaving space out of the cold war etc ended it .The Russkis had a few others like the "Golden Eagle " station manned observation sats and probably more and more secret stuff as well.(The first US sats- I think the Keyhole program -took a gazillion more pics than the whole U2 plane recce had done in years during the first weeks.)
There were alot more interesting space weapons like the US nuclear powered orbital bomber - The US wanted to have a few permanently hovering above Moscow just to set the mood there
.Its engines were tested ,but it never became a reality .
Then there is the L-5 society ,the group that worked for permanent orbital military bases at LaGrange -5 to dominate the skies and the world .
Today the race is more or less pewtering out due to proposed missile shields etc and other ground based systems .(boring )
but the good old NAZI Sanger bomber project supposedly is started up again by DARPA - the atmosphere skipping global reach heavy bomber thingy.
Militarization of space is a fun subject !