Nonetheless, unlike the MPAIAC, the party did not consider independence an immediate objective, but rather one to achieve in a long-term and gradual struggle.
In 1984 an internal crisis arose in the Canarian People's Union (UPC), leading to the de facto dissolution of the coalition (which would officially happen in 1986).
[6] During the 1984 crisis the PCC(p) was one of two the forces (the other one being the Canarian Party of the Popular Vanguard, and split of Communist Cells, led by the ex-MP Fernando Sagaseta) that opposed the dissolution of the coalition.
[7] During 1985 and 1986 the party campaigned against the permanence of the Canary Islands in the North Atlantic Treaty Organization (NATO).
After the NATO membership referendum of 1986 the party asked the Spanish government to declare the Canaries as an international neutral zone,[8] since the "leave" option had won in the islands.