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PSR 1055-52, a pulsar with a rotation period of 197 ms and a dynamic age of $5\times 10^5$ yr, has been observed with the {\sl ROSAT} Position Sensitive Proportional Counter and the High Resolution Imager. The results show that X-ray emission of PSR 1055-52 is strongly pulsed at the radio period. There is a phase shift of $\sim120^{\circ}$ between the softer and harder photons (below and above $\sim 0.5$ keV respectively). The spectrum is soft and black-body like with an additional hard tail. A neutron star with surface temperature of $\sim 7\times 10^5$ K and the power-law extension of the recently observed 100 MeV to 5 GeV gamma ray spectrum from GRO/EGRET (Fierro et al. 1993, preprint) fits the spectrum adequately. The contribution of a compact synchrotron nebula component above the 2$^{\prime\prime}$ resolution of the The High Resolution Imager is limited to less than 30\% of the point-like source.