A theory for determining the existence, number and position of limit cycles
in perturbed Hamiltonian systems, that depends on a small parameter, is pr
esented. The limit cycle emerges from the periodic trajectories surrounding
a centre of the unperturbed system. By means of this theory a sinusoidal o
scillator with a nonlinear element has been analysed. It is shown that only
the terms with odd degrees in the approximation polynomial of the nonlinea
r element's characteristic exert an influence on the initiation of limit cy
cles.