Аннотация:Abstract—A new analytical method has been developed for the study of mutual rotational oscillations (librations) of gravitating stellar ellipsoids that form double bars in disk galaxies. The double bar model is represented by a superposition of two concentric non-coaxial ellipsoids (bar 1 and bar 2) with different scales and masses. Two versions of the models are considered: with homogeneous bars and with a layered inhomogeneous outer bar 2. For each model, expressions for the mutual gravitational energy of ellipsoids are obtainedand the moment of forces between them is calculated; Lagrangians are constructed, and differential equations for nonlinear librations of the bars relative to the “median” plane are derived. Solutions of these equationsare found, and the frequencies and periods of librations are calculated both in the general nonlinear case and in the approximation of harmonic oscillations. The application of the method to the study of the dynamics of other subsystems of galaxies is discussed.