This paper reports results on the cellular and pulsating instabilities developed over the surface of expanding spherical premixed flames. Regarding the cellular instabilities, experimental data from time-resolved images of hydrogen-air flames exhibiting hydrodynamic and diffusional-thermal cells were used to determine the flame acceleration exponent α, defined through R(t)=R0+Atα. where A and R0 are constants. Results show that α seems to be bounded by the maximum value of 1.33 ± 0.03, which is approached regardless of the nature of the cells, and therefore suggesting the existence of a self-similar mode of propagation. Regarding pulsating instability, spiral waves and target patterns were experimentally observed over the flame surface in rich hydrogen-air, rich hydrogen-oxygen, and lean butane-oxygen-helium mixtures at elevated pressures. The transition boundary to instability was found to agree well with the Sivashinsky criterion, Ze(Le-1)>4(1+31/2) ≈ 10.9, provided local values are used in the evaluation of the Zel'dovich number, Ze, and the Lewis number, Le.