  We present here the X-ray observation of a Crab-like supernova remnant (SNR)
3C58 with ASCA. We find that the integrated energy spectrum over the nebula is
consistent with previous results, showing a power-law spectrum with the photon
index $\gamma = 2.2-2.4$ modified by interstellar absorption of about
$(3-4)\times 10^{21}{\rm cm^{-2}}$. Inclusion of a blackbody component which is
attributable to the central compact source significantly improves the spectral
fit. Stringent upper limits for any line emitting thin hot plasma are
established. We find for the first time that the nebular spectrum is harder in
the central part of the SNR, becoming softer toward the periphery, while the
absorption column is uniform across the nebula. Correspondingly, the nebular
size decreases with increasing photon energy which is a steeper function of
radius than that of the Crab nebula. The results are compared with synchrotron
energy loss models and the nature of the putative pulsar is discussed. Timing
analysis was performed to search for pulsed X-ray emission from the central
compact source. No significant pulsations are observed, and we present the
upper limit for the pulsed fraction.
