An adaptation of the sib pair method is given for testing the independence of transmission of Gm and the disease, using variable X (which gives information on the phenotypic identity of a sib pair for Gm). Then the joint distribution of IBD for HLA and X for Gm among affected sib pairs was derived under different two-locus models (multiplicative and other) in which one locus is strictly linked to HLA and the other to Gm. We also propose a test for a joint effect of HLA and Gm and whether this effect is multiplicative or not.