A computerized mathematical model of M. leprae populations during multiple drug therapy (MDT) was constructed. Relevant published information available to date was fed into it, and reasoned assumptions were made. From the model, it seems likely that MDT steadily selects bacteria resistant to the most powerful of the three drugs used: unless the individual bactericidal potencies of the drugs balance one another. If the drugs used have differing potencies, cure probably hinges on treatment being continued until all metabolically active bacteria are killed. Withdrawal of treatment before that could lead to relapse with bacteria resistant to the most powerful of the drugs used.