Association between disease and genetic polymorphisms often contributes critical information in our search for the genetic components of common diseases. Devlin and Roeder (1999) introduced genomic control, a statistical method that overcomes a drawback to the use of population-based samples for tests of association, namely spurious associations induced by population structure. In essence, genomic control (GC) uses markers throughout the genome to adjust for any inflation in test statistics due to substructure. To date genomic control (GC) has been developed for binary traits and bi- or multiallelic markers. Tests of association using GC have been limited to single genes. In this report, we generalize GC to quantitative traits (QT) and multilocus models. Using statistical analysis and simulations, we show that GC controls spurious associations in reasonable settings of population substructure for QT models, including gene-gene interaction. Through simulations we explore GC power for both random and selected samples, assuming the QT locus tested is causal and its specific heritability is 2.5 - 5%. We find that GC, combined with either random or selected samples, has good power in this setting, and that more complex models induce smaller GC corrections. The latter suggests greater power can be achieved by specifying more complex genetic models, but this observation only follows when such models are largely correct and specified a priori.