We consider the problem of motion of a spherically symmetric balloon satellite along an orbit with a moderate inclination in the neighborhood of a resonance caused by the joint influence of the Earth's oblateness and the pressure of light. An analytic approximate solution is constructed for a qualitative analysis of the problem. The correctness of the constructed analytical solution and the properties of the trajectories in the neighborhood of the saddle point separatrices of this solution are investigated using numerical integration of the nonsimplified system of equations of motion with a full set of perturbing factors. The effect of separatrix breakup accompanied by the appearance of regions of stochastic motion is studied. A description of quasi-random trajectories lying outside the stochasticity zone is given with the help of binary code. © Nauka/Interperiodica 2006.