The question of whether W UMa stars are contact binaries or not is still a problem. It is promising to see that the theoretical investigators are on the way to explain that and how contact binaries can really exist, even at age zero and with different masses. Let us assume — as is generally done — that the surfaces of the two components of a W UMa star can be set identical to the equipotential surfaces of the Roche model of two mass points. If these surfaces coincide with the limiting Roche lobe or even exceed it for a little amount, than we are justified to call the figure a contact system. However, it may well be that one star fills its critical lobe and the other one is a little bit below it, or even both components may be below their limiting lobes by a small amount. The uncertainty of the elements that can be derived from W UMa light curves for the time being does not allow for a definite decision. We have to look, therefore, for the possible differences between the light-curves of very close, not contact binaries and the variability of contact pairs.