  We present the analysis of archival data from the Advanced Satellite for
Cosmology and Astrophysics} (ASCA) of the supernova remnant (SNR) G39.2-0.3.
G39.2-0.3 has been sometimes characterized as a shell-like remnant in the
literature but our high-energy imaging and spectral analysis show the
unambiguous composite nature of the remnant. We find that part of the
contribution to G39.2-0.3's X-ray emission is distinctly non-thermal, best
described by a power law with a photon index ($2.53^{\rm +0.34}_{\rm -0.27}$).
The region of emission is consistent with a point source (extension consistent
with the point spread function of the detector at the off-axis angle of the
observation) and is roughly defined by a circle of radius of about 4 arcmin. A
second contribution comes from a thermal component which contributes flux
primarily at low energies. Despite the absence of any pulsed emission detected
from the compact source, we argue that the emission is most probably due to a
rotating compact object that is powering the detected synchrotron nebula within
the SNR. \\
