An asymptotic analysis involving the limit of large activation energy is presented for the study of thermal and chemical inhibition effects on premixed flames by heterogeneous flame suppressants. A formulation analogous to that for heterogeneous laminar flame is employed for evaluating the thermal effect, and extended to include the chemical effect in flame inhibition of decomposed particles or vaporized sprays. The propagation velocity of inhibited flames depends on the loading parameter 71, the particle size parameter 3,2, the nondimensional decomposition or latent heat of materials 3'3, the chemical effectiveness 3'4, and the decomposition rate parameter ~'0". The results for thermal inhibition (74 ~ 0) show that the response curve of the dependence of flame speed on parameters 3' 1 or ')2 has an S-shaped variation for flame suppressants satisfying 3'j > 71 * and 3,2 < 3,2", which correspond to a sufficient concentration of powders consisting of large particles. A slow decomposition rate, ~'0" "* 1. is essential for this S-shaped variation of flame speed. The results also show that the chemical effect on flame speeds appears as a virtual increase in the particle size parameter 3'2, by the factor l/X/l '-3't (1 --~'0")3'4, if the relative rate 3'4 of the chain-breaking reaction by gaseous inhibitors measured at the flame temperature is introduced.