Polytropic models of close and contact binary stars are constructed using a combination of perturbation techniques and a Laplace approximation previously applied to uniformly rotating stars. Synchronism between orbital and intrinsic angular velocity is assumed. Models are constructed including the effects of distortion for polytropes with indices fl = 1, , 2, 3 and 4. The conditions for the two stars to be just in contact are determined and contact models with a mass ratio of unity are constructed, right up to the limiting case when the stars fill all the available space inside the critical Roche surface surrounding the two stars. When the two stars are built on the same polytropic model contact stars with mass ratios different from unity are not possible.