Locus heterogeneity is a concern for quantitative trait locus mapping where phenotypes are likely to be influenced by more than one gene. We introduce a model which generalizes the locus heterogeneity model of Smith (1961) from dichotomous traits to quantitative traits and consider some test statistics for this model. The type I error rates and the power of these statistics are assessed through simulation studies. These statistics are applied to a linkage study of asthma genes.