  We extend Y.Eliashberg's $h$-principle to smooth maps of surfaces which are
allowed to have cusp singularities, as well as folds. More precisely, we prove
a necessary and sufficient condition for a given map of surfaces to be
homotopic to one with given loci of folds and cusps. Then we use these results
to obtain a necessary and sufficient condition for a subset of a surface $M$ to
be realizable as the critical set of some generic smooth map from $M$ to a
given surface $N$.
