  We give necessary and sufficient conditions of infinite determinacy for
smooth function germs whose critical locus contains a given set. This set is
assumed to be the zero variety X of some analytic map germ having maximal rank
on a dense subset of X. We obtain a result in terms of Lojasiewicz estimates
which extends, in particular, previous works by Sun & Wilson on line
singularities, and by Grandjean on singularities of codimension 1 or 2.
