Non-conformal supercurrents in six dimensions are described, which contain the trace of the energy-momentum tensor and the gamma-trace of the supersymmetry current amongst their component fields. Within the superconformal approach to ${cal N} = (1, 0)$ supergravity, we present various distinct non-conformal supercurrents, one of which is associated with an ${cal O}(2)$ (or linear) multiplet compensator, while another with a tensor multiplet compensator. We also derive an infinite class of non-conformal supercurrents involving ${cal O}(n)$ multiplets with $n > 2$. As an illustrative example we construct the relaxed hypermultiplet in supergravity. Finally, we put forward a non-conformal supercurrent in the ${cal N} = (2, 0)$ supersymmetric case.
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