Abstract: During the last years the study of the formally real fields has been a source of new interesting research. One of the most attractive aspects of these studies has been to find out the characteristics of the total Galois group of these fields attached to properties concerning the fact of being real. Among the pro finite groups the free profinite groups have appeared very frequently as the total Galois group of some fields ([ BNW], [D]). Haran and Jarden [HJ1] established the "real" analogue of the notion of a free profinite group. The aim of the present not is to examine closely a particular case of the real profinite groups; those having finitely many classes of involutions. Of course they are in connexion with fields having finitely many orderings. Of particular interest will be the pro-2-groups, as one can expect working on formally real fields. The results of this paper have been announced at the Conference on Quadratic Forms and Real Algebraic Geometry, Corvallis, July 1986 Ver menos