1. The extent to which an organism's immune system will tolerate tissue grafts from another organism.
2. A compatibility between the genotypes of donor and host such that a graft generally will not be rejected.

Normally, a graft from an unrelated individual is recognized as foreign by the recipient's white blood cells because the marker molecules (self-antigens) on the surface of the foreign cells differ from the recipient's marker molecules; therefore, the white cells are stimulated to mount an immune response against the foreign tissue.

Only certain close relatives share the same self-antigens, and can tolerate grafts of each other's tissues. The most important of these self-antigens are proteins coded by a complex cluster of genes called the Major Histocompatibility Complex (MHC).