This paper presents numerical and experimental studies on the onset and evolution of laminar cellular flames of CH4/O-2/CO2 (oxy-fuel) and CH4/air mixtures under adiabatic conditions, stabilized in the proximity of a flat-flame burner at atmospheric pressure. In the numerical simulations, a two-dimensional domain with periodicity at the transverse far field boundaries is resolved using a high accuracy finite difference method and employing a detailed chemical kinetic mechanism and detailed transport properties. In the experiments a specially designed adiabatic flat-flame burner, a so-called heat flux burner, is employed. A key parameter, the standoff distance between the flame front and the burner exit plate, is identified. A critical standoff distance is found, above which cellular flame instability is observed. It is shown that the critical standoff distance is closely related to the density ratio and the laminar flame thickness for each flame studied. The observed onset of cellular flames is governed by the hydrodynamic instability mechanism, which is generally suppressed by the burner when the flame is very close to the burner plate. Diffusive-thermal effects play an important role in the flame instability when the flame is far from the burner. The critical standoff distance has no clear correlation with the Lewis number, indicating a less significant effect of diffusive-thermal instability on the flames near the burner. (c) 2013 The Combustion Institute. Published by Elsevier Inc. All rights reserved.