We consider the motion of a spherically-symmetric balloon satellite perturbed by the Earth’s oblateness and solar radiation pressure. For equatorial satellite orbits and neglecting the Earth obliquity, the orbit-averaged equations for eccentricity and longitude of pericenter are integrable in quadratures (Krivov and Getino, 1996). The instability zone associated with the saddle separatrix in the phase space has been found and explored in depth. For semimajor axes about two Earth’s radii, and for area-to-mass ratios in the order of several tens cm2g−1, the amplitude and period of eccentricity oscillations may change nearly twofold under a small change of initial conditions or force parameters. We then restore the actual Earth obliquity of 235 and consider a spatial (non-integrable) problem. Near the saddle separatrix, a stochasticity zone appears that leads to large unpredictable eccentricity variations. The quasirandom motions of space balloons are investigated in terms of two-symbol (0-1) sequences by methods of stochastic celestial mechanics.