Recent Chandra ACIS-S observations have detected a point source at the cent
ral star of NGC 6543 and confirmed the point-source nature of the hard X-ra
y emission from NGC 7293. The X-ray spectra of both sources peak between 0.
5 and 1.0 keV and show line features indicating a thin plasma at temperatur
es of a few times 10(6) K. Their X-ray luminosities are 10(30) and 3 x 10(2
9) ergs s(-1), respectively. We have considered four different mechanisms t
o explain the nature of these sources. The X-ray emission from the central
star of NGC 6543 may originate from the coronal activity of an undetected c
ompanion star or from shocks in its fast stellar wind, while the hard X-ray
emission from NGC 7293 might be ascribed to an undetected dMe companion. F
ollow-up observations are needed to determine the existence and natures of
these stellar companions.