For the 1979 F2 championship, Cheever left Project Four and joined the Italian Osella team, taking three wins and fourth overall in their BMW-powered FA2. In Osella moved up to Formula One, Cheever piloting the team's Cosworth-powered FA1. However, the car was unreliable and Cheever managed just one finish all year, twelfth place at the team's home race in Italy. Switching teams repeatedly as he tried to climb his way up the grid, Cheever had five points-scoring finishes for the Tyrrell team in , and three podiums for Ligier the following year, including a second-place at the 1982 Detroit Grand Prix.