Crossbreeding programs are used intensively in livestock production systems. The aim of selective-breeding programs in many of these systems is to maximize crossbred performance, where selection is carried out within pure-lines using data from purebred animals. Genomic selection can be used to select purebreds for crossbred performance. Dominance is important in crossbreeding programs as it is the likely genetic basis of heterosis. The overall objective of this PhD project was to assess the possibilities of using dominance in genomic crossbreeding programs. Using stochastic simulations, response to selection in a two-way crossbreeding systems was investigated. Results showed that genomic selection can be used for efficient selection of purebreds for crossbred performance by addressing the factors that cause the genetic correlations between crossbreds and purebreds to be lower than one.