There were numerous countries during the Cold War period that didn't wanted to be part of one of the two sides, but instead wanted to be nonaligned, thus neutral. The reason for this was mainly that if they were aligned with one of the sides, they would have been involved in conflicts that are created by the others, usually the country leader of the alliance, US of NATO, or the Soviet Union of the Warsaw Pact. Apart from that, the country would have made numerous enemies instantly after choosing a side, so lot of leaders where trying to avoid the alliances, some successfully, some not. The best example for this is Yugoslavia during the reign of Tito, a country that was strong, between the two blocks, but acted by its own interests, not the others.