We have searched for X-ray emission from M-type giants and supergiants
listed in the Bright Star Catalogue (BSC) in the data of the ROSAT al
l-sky survey (RASS). These stars lie to the far right of the X-ray div
iding line and are thus not expected to be X-ray sources. Any X-ray de
tection would therefore violate the common paradigm of X-ray dark M-ty
pe giants beyond the X-ray dividing line. We found 11 BSC M-type giant
s and supergiants to coincide with RASS X-ray sources. While for 4 sta
rs the X-ray emission is very likely related to their cataclysmic or s
ymbiotic nature or can be attributed to a visual G-type companion, the
other 7 stars are candidates for intrinsic X-ray emission. Of these o
bjects, 3 have a rather large offset between optical and X-ray positio
n, so their proper identification with late-type giants is at least qu
estionable. For the remaining four stars, we obtained optical low-disp
ersion spectra in order to search for emission lines indicative of a p
ossible symbiotic nature. None of these stars shows any bright emissio
n lines, so they are probably quite normal M-type giants. We discuss p
ossible origins of X-ray emission in these stars and the importance of
evolutionary aspects.