Describe the other process that dominated world affairs during the years of decolonization. What forms did it take?

Decolonization of Asia and Africa took place between the years of 1945 and 1960. Several other processes took place concurrently, including the rise of Cold War tensions and the establishment of the Iron Curtain (a term made famous by Winston Churchill's 1946 address at an American University, with President Truman in attendance), and the corresponding rise in nationalism, or the emergence of the nation-state.
Decolonization marked the beginning of the end of European hegemony in world affairs. Newly independent countries in Asia and Africa practiced self-governance and were often remarkably stable. However, because these colonies had been exploited, many were poor. Additionally, the transition was not always peaceful. Especially in Asia, guerrilla fighters in Indonesia took up arms against the Japanese.
The United States was in a difficult predicament during the decolonization period, as nascent governments often appealed to them for military and economic support, but the United Stateswanted to resist the expansion of communism at any cost. The Truman Doctrine (issued in 1947) announced this new policy that promised to aid free people at the expense of supporting communist forces or guerrilla freedom fighters that espouse communist ideologies. Because of this motivation, the Truman Doctrine is often cited as the beginning of the Cold War.
The United States took a rather hard line against Communism under the administrations of both Truman and Eisenhower: the process of decolonization resulted in what the United States perceived as a power vacuum that the Communist Soviet Union could fill. The United States thus supplied aid to newly independent countries that supported Western governments.
In addition to the establishment of the Cold War, the creation of many new nations changed the political and economic global theater. For example, the United Nations grew from its 51 founding member states in 1945 to 127 members in 1970 (there are currently 192 members). The United Nations was designed to heighten economic security and promote international order, which became more important than ever with the emergence of so many new nations.