Tennilä was member of pro-Moscow opposition on Communist Party of Finland that was expelled from the party in 1986 and formed DeVa. He was chairman of Communist Party of Finland (Unity) in 1989–1990. Tennilä left the chairmanship and the party in 1990 as he joined Left Alliance.
Tennilä was internal critic of Left Alliance politics and was dismissed in 1995 from Left Alliance's parliamentary group as he opposed joining the Paavo Lipponen's first cabinet. He returned to list of Left Alliance in 1999 elections.
Tennilä has profiled himself as representative of Northern Finland and was in 2003 the most popular of the elected representatives in Lapland constituency. He has written poetry and children's books.