We consider the problem to classify function germs(C2, 0) (C, 0), that are equivariant simple with respect to nontrivial actions of the group Z3on C2and on C up to equivariant automorphism germs (C2, 0) (C2, 0).The complete classification of such germs is obtained in the case of nonscalar action of Z3on C2that is nontrivial in both coordinates. Namely, a germ is equivariant simple with respect to such a pair of actions if and only if it is equivalent to ine of the following germs:
 
 (x, y) x3k+1+ y2, k 1;
 (x, y) x2y + y3k1, k 2;
 (x, y) x4+ xy3
 (x, y) x4+ y5.