Asymptotic analyses are presented for spherical flame kernels (steady solutions) and slow flame expansion in mixtures near and beyond the flammability limits corresponding to a molecular diffusion coefficient of the limiting species greater than the thermal diffusivity, Lewis number smaller than unity, Le < I. The results concern also the dynamical quenching observed in micro-gravity experiments (self extinguishing flames) at large radius of flame expanding in non-flammable mixtures (beyond the flammability limits of planar flames). (C) 2016 The Combustion Institute. Published by Elsevier Inc. All rights reserved.