  In this paper the harmonic superspace action of the tensor multiplet of
$N=(1,0)$, $d=6$ supersymmetry is constructed which in the bosonic limit
reduces to the known Pasti-Sorokin-Tonin action for the self-dual tensor field.
The action involves, besides the potential containing the dynamical fields,
also an auxiliary tensor multiplet and a set of analytic superfields with gauge
PST scalar among them. For each of gauge symmetries of the PST action, a
superfield analog is found. The equations of motion are calculated and it is
shown in the bosonic limit that no extra degrees of freedom appear.
