Resonances between two stellar oscillation modes with nearly equal frequencies are studied in a nonlinear, isentropic approach. As governing equations, nonlinear amplitude equations for the time-behaviour of the amplitudes and phases of the resonant oscillation modes are derived from coupled-mode equations by means of a perturbation method. Expressions for the nonlinear coupling constants are derived in the approximation that the couplings are not influenced by modes other than the resonant ones. The amplitude equations are extended with two nonadiabatic terms involving the linear growth rates and the nonlinear self-saturations of the resonant modes. As stationary solutions of the amplitude equations, both monomode and double-mode solutions are possible. We studied analytically the existence and stability of the monomode stationary solutions.