The formation of interstellar molecules on the surfaces of dust grains is c
alculated in the framework of stochastic reaction kinetics. The master equa
tion and the state transition probabilities are defined, and the growth of
grain mantles following accretion and reaction of gas-phase species is comp
uted. The results are compared to the observed composition and structure of
interstellar ices. The differences between this approach to gas-grain kine
tics and previous work is discussed, and possible extensions of the theory
are outlined.