There definitely were nukes in Europe from both sides. In 1987 the US and USSR agreed to remove these intermediate-range nuclear missiles. (1)

Yeltsin had worked out an agreement with the former soviet republics that only Russia should retain nuclear arms, following the dissolvement of the USSR. Roughly 4/5ths of Nuclear arms were located on Russian soil following the collapse of the USSR in january 1992. The remaining 1/5th was spread over Ukraine, Kazakhstan and Belarus. The US mediated in an agreement in which the three republics agreed to dismantle the nuclear arms on their territory in return for financial reimbursement. (2)

1: R.R. Palmer, A History of Europe in the Modern World, §114 2: R.R. Palmer. A History of Europe in the Modern World, §118