Large-scale explosions of initially quiescent methane-ah and propane-air mixtures at atmospheric pressure are reported, in which the flame speed of a hemispherical flame is measured up to radii just beyond 3 m. A cellular flame is developed fairly soon and thereafter the flame speed increases continually with the square root of the time. The range of unstable wavelengths that wrinkle the flame increases as the flame propagates and this increases the flame speed. Two flame propagation regimes can be discerned. First, there is an initial stable regime, in which the flame is stabilized by thermo-diffusion and flame stretch, and the burning velocity is related to the Markstein length and rats of flame stretch. This is followed by a second regime in which, after a critical Peclet number has been attained, the flame is no longer stable, instabilities grow, wrinkle the flame, and increase the flame speed. Theoretical expressions for flame speed are presented for both regimes. That for the second rests on flame instability theory, with an increasing range of unstable wavelengths as the flame propagates. The theoretical predictions of flame radius with time over both regimes are in good agreement with those observed experimentally. Cell sizes are measured photographically as the flame progresses. These are fairly close to the theoretical wavelengths at which the rate of growth of the unstable flame amplitudes are a maximum. (C) 2001 by The Combustion Institute.