The perturbed motion in the neighbourhood of regular precessions of a dynamically symmetric satellite on a circular orbit is studied. The "Norma" specialized program package [1,2], intended for normalization of autonomous Hamiltonian systems by means of computer algebra, is used to obtain normal forms of the Hamiltonian. A full catalogue of non-resonant and resonant normal forms up to the 6th order of normalization is constructed for the case of hyperboloidal precession. The case of cylindrical precession, more complicated in analytical sense, is considered as well. Analytical expressions for coefficients of terms of the normal forms are derived as dependences on the frequencies and the initial physical parameters of the system. Though the intermediary expressions occupy megabytes of computer memory, the final normal forms are compact.