In (8) and (13) it has been shown that certain bisimple inverse semigroups, called bisimple ω-semigroups and bisimple Z-semigroups, can be represented as semigroups of ordered triples. In these cases, two of the components of each triple are integers, and the third is drawn from a fixed group. This representation is analogous to that given by the theorem of Rees (1, p. 94) concerning completely simple semigroups, and shares the same advantages.