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We consider, in the harmonic superspace approach, the six-dimensional N=(1,0)supersymmetric Yang-Mills gauge multiplet minimally coupled to a hypermultipletin an arbitrary representation of the gauge group. Using the superfieldproper-time and background-field techniques, we compute the divergent part ofthe one-loop effective action depending on both the gauge multiplet and thehypermultiplet. We demonstrate that in the particular case of N=(1,1) SYMtheory, which corresponds to the hypermultiplet in the adjoint representation,all one-loop divergencies vanish, so that N=(1,1) SYM theory is one-loop finite{\it off shell}.

One-loop divergences in 6D, N=(1,0) SYM theory