The evolution of contact binaries with common convective envelopes has been studied. Gravitational energy due to the mass exchange is taken into account in both stars, which turned out to be of crucial importance. Three qualitatively different evolutionary tracks have been found for an initial system 1.2M⊙ + 1.0M⊙. One of these corresponds to those found by Moss (1971), in which mass transfers, on a long time scale (≈5 × 108 yr), from the less massive component to the heavier. The second is similar to the solution found by Hazlehurst and Meyer-Hofmeister (1973), in which the evolution proceeds towards equal masses in a much shorter time scale (≈2 × 107 yr). The third possibility is similar to the first one, but its time scale is 10 times shorter (≈5 × 107 yr). The true evolutionary track may well oscillate randomly around the different solutions (rapid period changes).