Аннотация:The paper studies singularities of smooth functions in two variables invariant under the action of a finite group G by rotations. A classification of critical points appearing in typical parametric families of G-invariant smooth functions with at most two parameters is obtained, when |G| is different from 4. A criterion for reducibility of a smooth G-invariant function to a normal form is obtained, provided that the Taylor polynomial of degree |G| of the function is not a polynomial in x^2+y^2 and the Milnor G-multiplicity (respectively, G-codimension) of the singularity is less than |G| (respectively, |G|/2). A criterion for reducibility of a smooth parametric family of G-invariant functions to a normal from near a critical point of such type is obtained. The criteria are given in terms of partial derivatives of the function at the critical point.