In 1984 Alliot joined the Skoal Bandit RAM F1 team, but did not enjoy much in the way of success. After Jacques Laffite was injured at the 1986 British Grand Prix, Alliot took his place at Ligier, where he showed an improvement. He moved to Larrousse for 1987, but returned to Ligier in 1990, gaining a reputation for accidents. This led to heavy criticism from team members, other drivers and even sports commentators, such as James Hunt calling Alliot "one of the worst Grand Prix drivers ever to drive a Grand Prix car". He has the record of most race starts without any lead lap finish.