In this report, we present results of a genome-wide linkage scan using as a phenotype the number of externalizing symptoms associated with alcohol use disorders. Subjects were collected by the Collaborative Study on the Genetics of Alcoholism project from families in which at least three first degree relatives were affected by alcohol dependence. We use a novel non-parametric regression method based on kernel smoothing for our analysis. We report a statistically significant linkage close to the ADH gene cluster on Chromosome 4. We also obtain evidence for epistatic interaction between a region on Chromosome 1 and one on Chromosome 15. Although alcoholism as a covariate does not have any effect on the linkage scan, it has an effect on the epistatic interaction.