Results from the X-ray observations of pulsars with ASCA are presented. The surroundings of pulsars are investigated in detail taking advantage of ASCA's unique capabilities; high spectral resolution and a high throughput over a wide energy range from 0.4 keV to 10 keV. We detected diffuse emission sources in the vicinity of many pulsars, often with asymmetric structure. The high probability of finding such diffuse sources for many pulsars suggests that they exist universally for all the active pulsars, and that they are powered by the pulsars. The results of the ASCA observation of the two millisecond pulsars, PSR J0437-4715 and PSR B1821-24 are presented. They have very different characteristics. The energy spectrum of PSR J0437-4715 is best described by a blackbody with kT=0.27 keV. PSR B1821-24, on the contrary, has a hard X-ray spectra. A non-thermal sharp pulsed emission was detected.
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