Resistance to chemotherapies, particularly to anticancer treatments, is an increasingmedical concern. Among the many mechanisms at work in cancers, one of the most importantis the selection of tumor cells expressing resistance genes or phenotypes. Motivated bythe theory of mutation-selection in adaptive evolution, we propose a model based on acontinuous variable that represents the expression level of a resistance gene (or genes,yielding a phenotype) influencing in healthy and tumor cells birth/death rates, effects ofchemotherapies (both cytotoxic and cytostatic) and mutations. We extend previous work bydemonstrating how qualitatively different actions of chemotherapeutic and cytostatictreatments may induce different levels of resistance. The mathematical interest of ourstudy is in the formalism of constrained Hamilton–Jacobi equations in the framework ofviscosity solutions. We derive the long-term temporal dynamics of the fittest traits inthe regime of small mutations. In the context of adaptive cancer management, we alsoanalyse whether an optimal drug level is better than the maximal tolerated dose.