With the ability to measure thousands of related phenotypes from a single biological sample, it is now feasible to genetically dissect systems-level biological phenomena. The genetics of transcriptional regulation and protein abundance are likely to be complex, meaning that genetic variation at multiple loci will influence these phenotypes. Several recent studies have investigated the role of genetic variation in transcription by applying traditional linkage analysis methods to genomewide expression data, where each gene expression level was treated as a quantitative trait and analyzed separately from one another. Here, we develop a new, computationally efficient method for simultaneously mapping multiple gene expression quantitative trait loci that directly uses all of the available data. Information shared across gene expression traits is captured in a way that makes minimal assumptions about the statistical properties of the data. The method produces easy-to-interpret measures of statistical significance for both individual loci and the overall joint significance of multiple loci selected for a given expression trait. We apply the new method to a cross between two strains of the budding yeast Saccharomyces cerevisiae, and estimate that at least 37% of all gene expression traits show two simultaneous linkages, where we have allowed for epistatic interactions. Pairs of jointly linking quantitative trait loci are identified with high confidence for 170 gene expression traits, where it is expected that both loci are true positives for at least 153 traits. In addition, we are able to show that epistatic interactions contribute to gene expression variation for at least 14% of all traits. We compare the proposed approach to an exhaustive two-dimensional scan over all pairs of loci. Surprisingly, we demonstrate that an exhaustive two-dimensional scan is less powerful than the sequential search used here. In addition, we show that a two-dimensional scan does not truly allow one to test for simultaneous linkage, and the statistical significance measured from this existing method cannot be interpreted among many traits.