The present work is devoted to the analysis of the ill-posed inverse ellipsometric problem. Manifestations of the incorrectness of the problem are described for the case of ultrathin films. Special attention is given to the choice of the criteria for the optimal point. It is shown that an obvious and frequently used criterion expressed as a condition on difference functional S0 =< d**2, where d**2 is an average error in the measurement polarization angles, is practically useless in our case in the region strong incorrectness. New criteria for the choice of the optimal point are therefore suggested. As a result, the stable solution of the inverse ellipsometric problem is obtained which permits to study successfully the surface films in the thickness range 2–10 nm.