In terms of relations between the USSR and the USA, there weren't too many meaningful events. Ultimately Peaceful Co-existence was a failure, owing mainly due to the Cuban Missile Crisis.

Some important initiatives in the period were the 1955 Geneva Summit, and the 1959 visit of Khrushchev to the USA. However, a larger issue that came about during peaceful co-existence, was the Sino-Soviet split. Peaceful co-existence was something the USSR and China deeply disagreed on, and so perhaps the declaration denouncing the USSR in 1961, by the PRC is also worthy of being mentioned here.