Hogben [1932] gave the values for filial and fraternal correlations for matings involving two alleles in a panmictic population. The subject has been considered in great detail by Li [1955], but the known results are restricted to the case of two alleles. Consequently, if it is desired to compare a correlation derived from actual experimental data with a theoretical correlation computed on the basis of some genetic hypothesis, one can do so only if two alleles are involved. The present study will show how genetic correlations may be computed when more than two alleles are involved. While most results hold for n alleles, it will be convenient to employ n = 3 in some of the demonstrations. At a later time, it will be shown how to extend the results of Penrose [1933] and Stanton [1946] to the case of three alleles.