The appearance of time-dependent cellular structures in premixed flame propagation is known to occur in a parameter regime usually associated with the onset of steady cellular flame formation. We consider this phenomenon in the context of a model for downward flame propagation in vertical channels. In this model, the nonlinear evolution problem for the flame front describes flame propagation near the cellular instability threshold and predicts spinning solutions that arise from a certain class of steady, nonaxisymmetric mode interactions. However, unlike many combustion instabilities which can be anticipated from a linear stability analysis, a nonlinear stability analysis is required to predict these time-dependent solutions, which appear as either a secondary or tertiary infinite-period bifurcation from a bimodal cellular flame. In addition, it is shown that each admissible mode interaction is associated with a family of nonsteady flames and that each member of the family of spinning flames associated with the first pair of modes is orbitally stable.