LL- and TT-type vibratory micromechanical gyroscopes (MMG) are considered with regard for nonlinear dependence of the suspension resistance forces and electrostatic forces on the displacement of the MMG sensitive elements. Nonlinear differential equations for a MMG operating in the measuring mode are obtained. These equations contain both analytical and nonanalytical nonlinearities. The effect of these nonlinearities on the dynamics and precision of vibratory MMGs is studied. The use of the method of averaging revealed stable steady-state modes of vibratory MMGs. The corresponding resonance curves are constructed. The results obtained may find application in the design of devices of the types considered.