In the simple orbital resonance models we determine the spin and mass dependence of the twin peak frequencies for non-linear resonances of oscillations with the epicyclic and Keplerian frequencies or their combinations in the case of a general rational frequency ratio n:m, n > m. In the multi-resonant model, the twin peak resonances are combined properly to give the observed frequency set. In the first one, related probably to the neutron star binary systems, more instances of one resonance occur at more specific radii. In the second case, more resonances are sharing one specific radius, allowing for "cooperative" resonant phenomena in the field of black holes with a specific value of spin. In the third ("ugly") case, more resonances occur at more specific radii; we restrict our attention to the case of two such resonant radii.