Employing the formal similarity between the dispersion relations for the hydrodynamic (Darrieus-Landau) and the diffusive instabilities at the quenching threshold, a phenomenological model for the nonlinear evolution of the near-limit premixed flame is proposed. Numerical simulations of the model show that at sufficiently high Zeldovich and low Lewis numbers the cellular flame resulting from the diffusive instability exhibits a tendency towards self-fragmentation resembling that known to occur in near-limit low-Lewis-number systems. (c) 1995 The American Physical Society