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There is growing evidence of star formation in the vicinity of supermassive black holes (SMBHs) in galactic nuclei. A viable scenario for this process assumes infall of a massive gas cloud toward the SMBH and subsequent formation of a dense accretion disk, which gives birth to the young stars. Numerical hydrodynamical models indicate that this star formation process is rather fast and precedes full circularization of the accretion flow, i.e., the new stars are born on elliptic orbits. By means of direct numerical N-body modeling, we show in this paper that the nonzero eccentricity of the stellar disks around the SMBH leads to an onset of various types of the Kozai–Lidov oscillations of a non-negligible subset of individual orbits in the disk, showing a remarkable robustness of this classical mechanism. Among others, we demonstrate that under certain circumstances, the presence of an additional spherical cluster (which is generally known to damp Kozai–Lidov oscillations) may trigger such oscillations as a result of affecting the internal flow of the angular momentum through the disk. We conclude that the Kozai–Lidov oscillations are capable of substantially modifying the initial structure of the disk (its thickness and distribution of eccentricities, in particular). [ABSTRACT FROM AUTHOR]