Large 1-dimensional (ID) and 2-dimensional (2D) arrays of almost-linear and almost-lossless networks are investigated using the equivalent linearization technique of Kryloff and Bogoliuboff. The active element is assumed to be a distributed cubic nonlinear shunt conductance. It is demonstrated that an arbitrary number of nonresonant (or asynchronous) modes can be stably excited on a 2D oscillator, but only a single mode on a ID oscillator. Experiments confirm that a variety of multimode oscillations, resonant as well as nonresonant, are observed on 2D oscillators but not on ID oscillators.