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In this paper we describe a package XMOD  of functions for computing with crossed modules, their morphisms and derivations; $cat^1$-groups, their morphisms and sections, written using the GAP  group theory programming language. We have also enumerated the isomorphism classes of $cat^1$-groups in [1,4] and . We gave the application algorithms and some mathematical results on $cat^1$-group structures in . We also made a computational comment on pre-crossed modules, pre-$cat^1$ -groups and underlying grupoids in this paper.