  We prove that any flat family $(\mathcal{ F}_u)_{u\in U}$ of rank 2
torsion-free sheaves on a Gauduchon surface defines a continuous map on the
semi-stable locus $U^{\mathrm {ss}}:=\{u\in U \ |\ \mathcal{ F}_u\hbox{ is
slope semi-stable}\}$ with values in the Donaldson-Uhlenbeck compactification
of the corresponding instanton moduli space. In the general (possibly
non-K\"ahlerian) case, the Donaldson-Uhlenbeck compactification is not a
complex space, and the set $U^{\mathrm {ss}}$ can be a complicated subset of
the base space $U$ that is neither open or closed in the classical topology,
nor locally closed in the Zariski topology. This result provides an efficient
tool for the explicit description of Donaldson-Uhlenbeck compactifications on
arbitrary Gauduchon surfaces.
