Fraternal party literally means brother party. The term refers to a political party

Political party

A political party is a political organization that typically seeks to influence government policy, usually by nominating their own candidates and trying to seat them in political office. Parties participate in electoral campaigns, educational outreach or protest actions...

 officially affiliated with another, often larger and/or international, political party or governmental party.

In 1960s

1960s

The 1960s was the decade that started on January 1, 1960, and ended on December 31, 1969. It was the seventh decade of the 20th century.The 1960s term also refers to an era more often called The Sixties, denoting the complex of inter-related cultural and political trends across the globe...

, Communist parties

Communist party

A political party described as a Communist party includes those that advocate the application of the social principles of communism through a communist form of government...

 in charge of states

Communist state

A communist state is a state with a form of government characterized by single-party rule or dominant-party rule of a communist party and a professed allegiance to a Leninist or Marxist-Leninist communist ideology as the guiding principle of the state...

 often had fraternal parties in other countries than the one(s) in which they were organised. A major example was the Communist Party of China

Communist Party of China

The Communist Party of China , also known as the Chinese Communist Party , is the founding and ruling political party of the People's Republic of China...

, which exercised enormous influence over the New Left

New Left

The New Left was a term used mainly in the United Kingdom and United States in reference to activists, educators, agitators and others in the 1960s and 1970s who sought to implement a broad range of reforms, in contrast to earlier leftist or Marxist movements that had taken a more vanguardist...

 and New Communist Movement

New Communist Movement

The New Communist Movement ' was a Marxist-Leninist political movement of the 1970s and 1980s in the United States. The term refers to a specific trend in the U.S. New Left which sought inspiration in the experience of the Russian Revolution of 1917, the Chinese Revolution, and the Cuban...

 of the 1960s and 1970s. In The Modern History Sourcebook, there is a 1964 statement by the Romanian Workers' Party in which they caution, "In discussing and confronting different points of view on problems concerning the revolutionary struggle or socialist construction, no party must label as anti-Marxist, anti-Leninist the fraternal party whose opinions it does not share." http://www.fordham.edu/halsall/mod/1964romania-china.html