We present ROSAT PSPC pointed observations of the 50 Myr old #alpha# Per open cluster. The X-ray observations, which were carried out as a raster scan, cover an area of about 10 deg"2. In total, we detect about 160 X-ray sources, 88 of which have an optical counterpart (with 30 arcsec) associated with #alpha# Per cluster candidates. Within the central region of our field of view, which is characterized by a limiting sensitivity L_X #approx# 10"2"8"."8"-"2"9 erg sec"-"1, we detect basically all late-F, G and K stars, while the detection rate among the M dwarfs is on the order of 60%. Given the sensitivity of our X-ray observations, the lower detection rate among the very low mass objects is consistent with the ROSAT results obtained for the Pleiades cluster. Although stars in each color range show a large spread in X-ray luminosity, the maximal X-ray luminosities appear to decrease from the range of late-F-G type stars to the M-type dwarfs. A comparison of the X-ray luminosity distribution functions (XLDF) for our #alpha# Per sample and the Pleiades indicates that F and G-type stars in #alpha# Per are, as a whole, more X-ray luminous than their older counterparts in the Pleiades. On the other hand, no significant difference is found between the distributions of the K and M-type dwarfs in the two clusters. We argue that this finding is a consequence of the longer spin-down timescales of later-type objects, and hence of the fact that there are more rapid rotators among G stars in #alpha# Per than in the Pleiades, while this is not the case for K and M dwarfs. (orig.)SIGLEAvailable from TIB Hannover: RN 9303(329) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman