Аннотация:The equation of plane oscillations of a satellite is a Hamiltonian system with one degree of freedom and 2Pi-periodic dependence on time and on x_1. It contains two parameters epsilon and e, one of which (epsilon) is small. The unperturbed system is linear. Solutions that correspond to cycles of the Poincare map on a cylinder (x_1 mod 2Pi, x_2) are called Lissajous solutions. Their stability and bifurcations with parameter e changing are studied by the averaging method. It is shown how degenerate cases, where calculation of higher order terms is needed, arise in a natural way. Sufficient truncations of the normal form for those cases are described.