<b>Abstract</b>— <p>By calculating the Lyapunov characteristic exponents in the hierarchical three-body problem (star–planet–planet’s satellite), an analysis of the applicability of a number of criteria for estimating the maximum possible value of the semimajor axis <i>a</i>_crit of a satellite’s orbit was carried out, corresponding to its long-term stable orbital dynamics. It has been shown that the empirical criterion from the work (Domingos et al., 2006), which is often used to determine potential orbits of exomoons (satellites of exoplanets), significantly overestimates the value of <i>a</i>_crit. In a planar problem for a prograde orbit (the directions of orbital motion of the planet and satellite coincide) of an exomoon, when estimating <i>a</i>_crit the criterion proposed by Rosario-Franco et al. (2020) works better, for the retrograde orbit of the exomoon, the criterion from the work (Quarles et al., 2021) works better. If the angle between the orbital planes of the planet and the satellite can be significant (&gt;30°), a reliable estimate for <i>a</i>_crit can be obtained by numerical modeling of the long-term orbital dynamics of the exomoon and using rigorous methods of motion stability analysis (calculation of Lyapunov characteristic exponents, the MEGNO parameter, etc.).</p>