In this paper, an invariant manifold approach is introduced for the generat
ion of reduced-order models for nonlinear vibrations of multi-degrees-of-fr
eedom systems. In particular, the invariant manifold approach for defining
and constructing nonlinear normal modes of vibration is extended to the cas
e of multi-mode manifolds. The dynamic models obtained from this technique
capture the essential coupling between modes of interest, while avoiding co
upling from other modes. Such an approach is useful for modeling complex sy
stem responses, and is essential when internal resonances exist between mod
es. The basic theory and a general, constructive methodology for the method
are presented. It is then applied to two example problems, one analytical
and the other finite-element based. Numerical simulation results are obtain
ed for the full model and various types of reduced-order models, including
the usual projection onto a set of linear modes, and the invariant manifold
approach developed herein. The results show that the method is capable of
accurately representing the nonlinear system dynamics with relatively few d
egrees of freedom over a range of vibration amplitudes.