The dynamics of particles in a Penning trap with a rotating dipole electric field and a buffer gas is considered. A transition is made to a coordinate system that rotates together with the electric field, which makes it possible to reduce the system of ordinary differential equations with periodic coefficients to a linear differential system with a constant matrix. Using one of the modifications of the Hurwitz stability criterion-the Lienard-Chipart criterion, the stability analysis (according to Lyapunov) of particle motions in the trap is carried out and the stability regions in the trap parameter space are found.Calculations were carried out for a trap with “typical” main parameters. The biggest degree of stability was obtained at frequencies of rotation of the field close to “resonant”. Small relative deviations from these frequencies led to a significant decrease in the degree of stability and loss of stability at “small” values of the amplitude of the rotating field. At the same time, it was possible to partially compensate this by increasing the amplitude of the rotating field, but only to certain limits, after which stability was again lost.