In the present paper we consider spherically and axially symmetric stellar system models in order to examine the character of orbits of stars moving in the gravitational field. We study orbits in the meridian plane for the model with the massive nucleus varying values of the structural parameters, as well as two integrals of motion. In an attempt to distinguish regular and chaotic motions we use surfaces of section. We numerically investigate the orbits of star cluster moving in the plane of the galaxy in a circular orbit. The impact of initial conditions on the star movements and probability to escape from the cluster are examined. Calculations of star orbits for various initial values of energy and momentum has been done. Simulations showed that retrograde orbits of stars are more stable than regular ones.