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The stability of the motion of planet satellites is considered in a model of the general three‐body problem (sun–planet–satellite). ‘Sundman surfaces’ are constructed, by means of which the concept of ‘Sundman stability’ is formulated. A comparison of Sundman stability with the results of Golubev’s c2h method and with Hill’s classical stability in the restricted three‐body problem is performed. The constructed Sundman stability regions in the plane of ‘energy–moment of momentum’ parameters coincides with the analogous regions obtained by Golubev’s method, with the value (c2h)cr. Construction of Sundman surfaces in the three‐dimensional space of the specially selected coordinates xyR is carried out by means of the exact Sundman inequality in the general three‐body problem. Determination of the singular points of surfaces and regions of possible motion and Sundman stability analysis are implemented. It is shown that the singular points of the Sundman surfaces in the coordinate space xyR lie in different planes. The Sundman stability of all known natural satellites of planets is investigated. It is shown that a number of natural satellites that are stable according to Hill and also some satellites that are stable according to Golubev’s method are unstable in the sense of Sundman stability.

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