  We consider, in the harmonic superspace approach, the six-dimensional N=(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 N=(1,1) SYM
theory, 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}.
