  We examine nonlinear oscillations of slender tori in the vicinity of black
holes and compact stars. These tori represent useful probes of the complicated,
nonlinear dynamics of real accretion disks and provide at least qualitative
understanding of their oscillations. We demonstrate that epicyclic modes of
such tori are weakly coupled due to the pressure and gravitational forces. We
explore all possible resonances between two epicyclic modes up to the fourth
order. We show that the strongest resonance between axisymmetric modes is 3:2.
In addition, any resonance between an axisymmetric and a non-axisymmetric mode
is excluded due to axial and equatorial-plane symmetries of the equilibrium
torus. We examine a parametric excitation of vertical axisymmetric oscillations
by radial oscillations in the 3:2 resonance. We show that the resonance may be
significant only for high-amplitude radial oscillations.
