The structure of late-type contact binary systems of the W UMa type is investigated using the Lucy ( 68a) model with a common convective envelope. However more recent opacities than those adopted by Lucy are used. Some differences are found, but we agree that no zero age systems with unequal components are to be found with a normal Population I composition. Zero age systems are found for extreme Population I compositions. The effect of changing the mixing length theory is found to be small. Preliminary investigations of the effects of the evolution of the primary from the ZAMS are made, and it may be possible to produce cool systems of low mass ratio this way. However the positions of some observed systems in the period-colour diagram cannot be explained.