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[References: 35 tit.]

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