The optimized optical structure of the NICA collider is considered. Studies and calculation methods of the stability region of the motion of charged particles in the collider—the dynamic aperture—are presented. The influence of the magnetic-field nonlinearities, in particular, the fringe fields of the magnetic elements on the dynamic aperture, is considered. The dependences of the dynamic aperture on optical properties of the collider, the choice of the working point of betatron frequencies, and tuning parameters of the beam-interaction region are shown. The methods for compensating the effect of the fringe fields on the stability of beam dynamics are discussed.