The nearby spiral galaxy M33 was observed for 35 ks with the high-reso
lution imager on ROSAT in 1992 January and August. We find 27 X-ray so
urces more luminous than 6 x 10(36) ergs s(-1) within 17.5' of the nuc
leus, of which 12 were discovered by the Einstein Observatory. Three o
f the ROSAT sources are coincident with giant H II regions, and seven
are coincident or nearly coincident with supernova remnants. There is
evidence for long-term variability between the Einstein and ROSAT obse
rvations in three sources, one of which was not detected in the ROSAT
observations. Aside from an eclipsing binary X-ray source discovered b
y the Einstein Observatory, there is no evidence for variability withi
n the ROSAT observations. Of the 120 cataloged holes in the H I layer
in the field of view, two have significant X-ray emission. One is coin
cident with the giant H II region IC 133 while the other appears to be
due to the chance superposition of a strong X-ray point source. Such
holes are thought to be created by energetic stellar winds and superno
vae from massive stars in young associations. We detect diffuse X-ray
emission with a luminosity of about 10(39) ergs s(-1) which may trace
the spiral arms within 10' of the nucleus.