Observations of asteroids at the Crimean astrophysical observatory (CrAO) were conducted since the 1980s. The Maksutov 50-cm telescope and TV installation were used, allowing to automate the process of observation. Brightness of asteroid was investigated in VBR bands simultaneously. The resulting light curves are processed on a computer by the method of frequency analysis, which reveals the hidden periodicity of changes of asteroid brightness. According to the observations of the asteroid brightness of 39 Laetitia at CrAO it was confirmed that this asteroid is a binary. The satellite orbital period of the binary system of 39 Laetitia and the period of axial rotation of components have been identified with the observed frequencies. In this paper we assume that the satellite has not yet fully stabilize its orientation with respect to its orbital radius vector and there is residual libration in the orbital plane with a small amplitude. The first six har-monics of the expansion of the gravitational potential of the satellite were taken into account. Emerging from their influence the theoretical values of the libration period due to these harmonics were compared with those obtained from observations by frequency analysis of light curves. It was proven that there is a sufficiently close match with one of the periods obtained by frequency analysis of light curves. This cir-cumstance can be seen as confirmation of the hypothesis of the exist-ence of small libration of the satellite in the binary system of 39 Lae-titia. The dynamics of this binary system deserves a more complete study.