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In this note wve attack the problem of classifying a pair of abelian group homomorphisms by introducing a construction which we call "the derived equaliser". After developing fairly simple methods for the calculation of these objects, we work an example in a simple case. Introduction. The simplicity of the classification, up to isomorphism, of group homomorphisms by their kernels and cokernels tends to overshadow the problem for two or more homomorphisms. Recall that the First Isomorphism Theorem allows one to write any homomorphism as a composite of an epimorphism and an inclusion of a subgroup; the epimorphism is determined (up to isomorphism of group homomorphisms) by its kernel, and the inclusion can either be regarded as an invariant itself or it can be determined by its cokerneL. The diagram

The first derived equaliser of a pair of abelian group homomorphisms