We use a mathematical model to understand (from 1996 to 2001) and to predict (from 2001 to 2005) the evolution of the epidemic of drug-resistant HIV in San Francisco. We predict the evolutionary trajectories for 1,000 different drug-resistant strains with each strain having a different fitness relative to a drug-sensitive strain. We calculate that the current prevalence of resistance is high, and predict it will continue to rise. In contrast, we calculate that transmission of resistance is currently low, and predict it will remain low. We show that the epidemic of resistance is being generated mainly by the conversion of drug-sensitive cases to drug-resistant cases, and not by the transmission of resistant strains. We also show that transmission of resistant strains has not increased the overall number of new HIV infections. Our results indicate that transmission of resistant strains is, and will remain, a relatively minor public health problem.