it is not federalism as federalism only has 43 of 123 nations
multi-party
Congress
The US political party system, for most of its history, has had a two party system. Most is a key word here. Bringing the question to today's US party system, the Democratic and Republican parties dominate the US. With that said, it should be noted that within each party are various "wings". Meaning in the Democratic Party for example purposes, there is a left wing of the party and a moderate wing and a conservative wing. This is true for the Republican party as well.
democratic
Today the leading political party in Brazil is PT (in portuguese: Partido dos Trabalhadores, english: Worker's Party). That´s the political party of the President Lula. The Political position of PT is the Left.
The tea party and the republican party.
Vietnam has a one-party socialist republic system of government. The Communist Party of Vietnam is the dominant political party, and the government is led by the General Secretary of the party. Although there are other political parties allowed, the Communist Party holds significant power.
The United Kingdom can be said to have three significant political parties. These include: The Conservative Party, The Labor Party, and the Liberal Party.
The Green party
The Republican Party, but not as you know it today
Typically in today's political system, the two major parties, the RNC and the DNC have their own primaries to decide who is running on party funds.
Russia's communist part today is known as the Communist Party of the Russian Federation. It's the second largest political party in Russia today.