AbstractArrays of negative resistance tunneling elements can support multimode, multistate oscillations and have been proposed for information processing applications. Published studies have analyzed nonresonant mode interactions by treating the nonlinear tunneling currents as small perturbations on the time‐average behaviour of a linear lossless array, but they have neglected the effects of linear resistive losses. For an array of superconductive tunnel junctions, these resistive losses, treated using the same perturbation formalism, are shown to give rise to mode combinations in which some modes have negative energies, leading to the conclusion that such mode combinations cannot exist physically. Order of magnitude quantitative estimates indicate that such mode limiting effects might well occur in practical arrays and suggest how the array geometry might be modified to minimize these effect