A workable algorithm is proposed for reducing the Poincaré — Pontriagin generating equation which determines periodic solutions for small perturbations of two-dimensional Hamiltonian systems to the special (standard) form for the class of equations x ̈ + αx + βx 3 = εf (x, x ̈ ), ε ⪡ 1 where f is a polynomial. As an example of application, the problem of estimating the number of cycles, in particular of stable periodic solutions, i.e. of auto-oscillating modes, is considered. Results are illustrated on a specific example.