This study predicts the ultimate probability of survival of a newly arisen drug resistant mutant in a population of malaria parasites, with a view to understanding what conditions favour the evolution of drug resistance. Using branching process theory and a population genetics transmission model, the probabilities of survival of one- and two-locus new mutants are calculated as functions of the degree of drug pressure, the mean and variation in transmission rate, and the degree of natural selection against the mutant. Probability of survival increases approximately linearly with drug pressure, the slope of the line increasing with mean transmission rate. Thus increased drug pressure, especially in combination with high transmission rates, strongly favours the evolution of drug resistance. These conclusions also hold for the case of multiple drug resistance where it is coded for by two unlinked loci: the greater effective recombination breakdown in high transmission areas is counteracted by greater effective selection so that the net effect of higher transmission rates is to favour the evolution of multiple drug resistance. High variability in transmission rate and natural selection against the mutants are unfavourable to mutant survival, though these are relatively weak forces.