  We present XMM-Newton and Chandra observations of two low-metallicity
cometary blue compact dwarf (BCD) galaxies, Mrk 59 and Mrk 71. The first BCD,
Mrk 59, contains two ultraluminous X-ray (ULX) sources, IXO 72 and IXO 73, both
associated with bright massive stars and H II complexes, as well as one fainter
extended source associated with a massive H II complex at the head of the
cometary structure. The low-metallicity of Mrk 59 appears to be responsible for
the presence of the two ULXs. IXO 72 has varied little over the last 10 yr,
while IXO 73 has demonstrated a variability factor of ~4 over the same period.
The second BCD, Mrk 71, contains two faint X-ray point sources and two faint
extended sources. One point source is likely a background AGN, while the other
appears to be coincident with a very luminous star and a compact H II region at
the "head" of the cometary structure. The two faint extended sources are also
associated with massive H II complexes. Although both BCDs have the same
metallicity, the three sources in Mrk 71 have X-ray luminosities ~1-2 orders of
magnitude fainter than those in Mrk 59. The age of the starburst may play a
role.
