In this paper we study dynamical systems generated by a gonosomal evolution
operator of a bisexual population. We find explicitly all (uncountable set) of fixed points of the
operator. It is shown that each fixed point has eigenvalues less or equal to 1. Moreover, we show that
each trajectory converges to a fixed point, i.e. the operator is reqular. There are uncountable family of
invariant sets each of which consisting unique fixed point. Thus there is one-to-one correspondence
between such invariant sets and the set of fixed points. Any trajectory started at a point of the invariant
set converges to the corresponding fixed point.