  We present X-ray observations of two young energetic radio pulsars, PSRs
B1046-58 and B1610-50, and their surroundings, using archival data from the
Advanced Satellite for Cosmology and Astrophysics (ASCA).
  The energetic pulsar PSR B1046-58 is detected in X-rays with a significance
of 4.5 sigma. The unabsorbed flux, estimated assuming a power-law spectrum and
a neutral hydrogen column density N_H of 5E21 cm^-2 is (2.5 +/- 0.3) x 10E-13
ergs/cm^2/s in the 2-10 keV band. Pulsed emission is not detected; the pulsed
fraction is less than 31% at the 90% confidence level for a 50% duty cycle. We
argue that the emission is best explained as originating from a pulsar-powered
synchrotron nebula. The X-ray counterpart of the pulsar is the only hard source
within the 95% error region of the previously unidentified gamma-ray source 3EG
J1048-5840. This evidence supports the results of Kaspi et al. (1999), who in a
companion paper, suggest that PSR B1046-58 is the counterpart to 3EG
J1048-5840.
  X-ray emission from PSR B1610-50 is not detected. Using similar assumptions
as above, the derived 3 sigma upper limit for the unabsorbed 2-10 keV X-ray
flux is 1.5E-13 ergs/cm^2/s. We use the flux limit to estimate the pulsar's
velocity to be less than ~170 km/s, casting doubt on a previously reported
association between PSR B1610-50 and supernova remnant Kes 32. Kes 32 is
detected, as is evident from the correlation between X-ray and radio emission.
The ASCA images of PSR B1610-50 are dominated by mirror-scattered emission from
the X-ray-bright supernova remnant RCW 103, located 33' away.
  We find no evidence for extended emission around either pulsar, in contrast
to previous reports of large nebulae surrounding both pulsars.
