Let X be an analytic variety f a function germ which is finitely determined with respect to X. In this talk we give conditions under which the following relative analog of the well known theorem of K. Saito holds: equality of the relative Milnor and Tjurina numbers (also called Bruce-Roberts numbers) is equivalent to the quasihomogeneity of the pair (f,X) in an appropriate coordinate system and with respect to the same positive rational weights