  Recent surveys of the Local Group spiral Galaxies M31 and M33 with XMM-Newton
yielded a large number of X-ray sources. As part of the effort to identify and
classify the objects responsible for this X-ray emission, we have obtained
optical spectra of the brightest optical counterparts of the identified X-ray
sources, using the 1.3m Skinakas Telescope. Most of these objects are
foreground star candidates. The purpose of the present study is to confirm this
identification and to explore the compatibility between the optical spectral
classification and the observed X-ray properties of the sources. We have
obtained optical spectra for the 14 brightest optical counterparts of X-ray
sources identified by XMM-Newton in the direction of M31 and for 21 optical
counterparts in the direction of M33, using the 1.3m Skinakas telescope in
Crete, Greece. All of the M31 sources and all but one of the M33 sources were
confirmed to be foreground stars, of spectral types between A and M. One of the
stars is a late M dwarf with H-alpha emission, a flare star, also displaying
strong X-ray variability. One of the M~33 sources (lying within the D25
ellipse) corresponds to a previously known background galaxy, LEDA 5899.
