Methods to formulate and maximize response to selection for a quantitative trait over multiple generations when information on a quantitative trait locus (major gene) is available were developed to investigate and optimize response to selection in mixed inheritance models. Deterministic models with and without gametic phase disequilibrium between the major gene and other genes that affect the trait (polygenes) were considered. Genetic variance due to polygenes was assumed constant. Optimal control theory was used to formulate selection on an index of major gene effects and estimates of polygenic breeding values and to derive index weights that maximize cumulative response over multiple generations. Optimum selection strategies were illustrated using an example and compared with mass selection and with selection with full emphasis on the major gene (genotypic selection). The latter maximizes the single-generation response for a major gene with additive effects. For the example considered, differences between selection methods in cumulative response at the end of a planning horizon of 5, 10, or 15 generations were small but responses were greatest for optimum selection. Genotypic selection had the greatest response in the short term but the lowest response in the longer term. For optimum selection, emphasis on the major gene changed over generations. However, when accounting for variance contributed by the major gene, optimum selection resulted in approximately constant selection pressure on the major gene and polygenes over generations. Suboptimality of genotypic selection in the longer term was caused not so much by gametic phase disequilibrium but rather by unequal selection pressure on the major gene (and, therefore, on polygenes) over generations, as frequency and variance at the major gene changed. Extension of methods to more complex breeding structures, genetic models and objective functions is discussed.