Steady-state vibrations of a class of nonlinear discrete systems with an arbitrary number of degrees of freedom are studied. The co-ordinates of the system are first transformed to the principal co-ordinates corresponding to the linear part of the system. A perturbation scheme is used to obtain the solutions. Some special effects of the ratios of the linear natural frequencies on the qualitative nature of the solutions are demonstrated. Solutions are obtained for some specific problems and the results are checked against those obtained from an analog-type computer.