After ten years in the National Assembly, Cavayé was elected as its Second Vice-President in 1983. In 1985, when President Paul Biya transformed the CNU into the CPDM, Cavayé was retained as a member of the CPDM Central Committee. He served as Second Vice-President of the National Assembly for five years, departing the legislature at the end of the parliamentary term in 1988 and instead becoming Prefectoral Assistant of Diamaré. He returned to the National Assembly in the March 1992 parliamentary election and was then elected as President of the National Assembly.
Cavayé was re-elected to the National Assembly in the May 1997 parliamentary election and was then re-elected for a second term as President of the National Assembly in mid-1997. After Paul Biya was re-elected in the October 1997 presidential election amidst an opposition boycott, Cavayé said at the opening of a parliamentary session on 1 November 1997 that deputies should « respect the institutions of the Republic » and « be worthy representatives of the sovereign people », but the opposition deputies ignored his admonition and boycotted Biya’s swearing-in ceremony on 3 November.
At the opening of a parliamentary session on 8 November 2001, Cavayé strongly criticized secessionist tendencies among the Anglophone population, saying that secessionism threatened national stability and that the National Assembly would not tolerate it. Following the 2002 parliamentary election, the CPDM Political Bureau again selected Cavayé as the party’s candidate for the post of President of the National Assembly. He was then re-elected in August 2002; there were no other candidates for the position, and Cavayé received 132 votes in favor and 27 against, while four deputies abstained from the vote. In November 2005, he urged deputies to take an active role in the fight against corruption.
Explaining his decision to run again in the July 2007 parliamentary election, Cavayé said that he was passionate about his parliamentary duties and that he wanted to « help President Paul Biya honour his electoral pledge of major changes to the Cameroonian people during the 2004 presidential polls ». Cavayé was again re-elected to the National Assembly as a CPDM candidate in the Mayo-Sava Constituency of Far North Province.
He was re-elected as President of the National Assembly on 4 March 2010. He was the only candidate and received 141 votes, while 16 deputies spoiled their votes.
As the traditional chief of Mada, Cavayé attended the National Forum of Traditional Rulers of Cameroon in March 2010. He was designated as Honorary President of the Forum and presided over its opening and closing ceremonies. At the Forum, which resulted in the creation of the National Council of Traditional Rulers of Cameroon, Cavayé discussed the venerable and enduring role of traditional chiefs and stressed that they worked cooperatively with the state administration, recognizing the authority of the state’s laws. Cavayé said that the National Council was not a political organization and should never act as a parallel authority alongside the state; instead, he defined the Council as an institution dedicated to cooperation, promoting traditional culture, and assisting the state administration in its work for the benefit of the population. The Council subsequently issued a statement calling on President Biya to stand for re-election in the 2011 presidential election and vowing to support Biya’s work in developing the country.
In the September 2013 parliamentary election, Cavayé was re-elected to the National Assembly. When the National Assembly began meeting for its new parliamentary term, he was re-elected as President of the National Assembly on 4 November 2013. Cavayé received the votes of 150 deputies, while 23 deputies cast invalid votes.
Cavaye has four wives and 15 children.