G328.4+0.2 is a moderately small ( 5 ^ { \prime } \times 5 ^ { \prime } ) Galactic radio supernova remnant ( SNR ) at a distance of at least 17 kpc that has been long suggested to be Crab-like . Here we report on the detection with ASCA of the X-ray emission from the SNR . The X-ray source is faint with an observed flux of ( 6.0 \pm 0.8 ) \times 10 ^ { -13 } erg s ^ { -1 } cm ^ { -2 } over the 2–10 keV band . The emission is heavily cut-off at low energies and no flux is detected below 2 keV . Spectral analysis confirms that the column density to the source is indeed large , N _ { H } \sim 10 ^ { 23 } atoms cm ^ { -2 } , and consistent with the total column density of hydrogen through the Galaxy at this position . Good fits to the spectrum can be obtained for either thermal plasma or nonthermal power-law models , although the lack of detected line emission as well as other evidence argues against the former interpretation . The power-law index we find , \alpha _ { P } = 2.9 ^ { +0.9 } _ { -0.8 } , is consistent with other Crab-like SNRs . In the radio band G328.4+0.2 is nearly as luminous as the Crab Nebula , yet in the X-ray band luminosity it is some 70 times fainter . Nevertheless its inferred soft X-ray band luminosity is greater than all but the brightest pulsar-powered synchrotron nebulae and implies that G328.4+0.2 contains a rapidly spinning , as yet undetected , pulsar that is losing energy at a rate of \sim 10 ^ { 38 } erg s ^ { -1 } .