1. Statement of the problem and main result. Consider selfadjoint opera-

A family of selfadjoint operators of the Friedrichs model is considered. These symmetric type operators have one singular point, zero of order m. For every m> 3/2, we construct a rank 1 perturbation from the class Lip1 such that the corresponding operator has a sequence of eigenvalues converging to zero. Thus, near the singular point, there is no singular spectrum finiteness condition in terms of a modulus of continuity of a perturbation for these operators in case ofm> 3/2