  The aim of this paper is to describe a class of conservative systems on $S^2$
possessing an integral cubic in momenta. We prove that this class of systems
consists off the case of Goryachev-Chaplygin, the one-parameter family of
systems which has been found by the author in the previous paper
(dg-ga/9711005) and a new two-parameter family of conservative systems on $S^2$
possessing an integral cubic in momenta.
