  (Abridged) Classical novae (CNe) have recently been reported to represent the
major class of supersoft X-ray sources (SSSs) in the central region of our
neighbour galaxy M 31. We carried out a dedicated monitoring of the M 31
central region with XMM-Newton and Chandra in order to find SSS counterparts of
CNe, determine the duration of their SSS phase and derive physical outburst
parameters. We systematically searched our data for X-ray counterparts of CNe
and determined their X-ray light curves and spectral properties. Additionally,
we determined luminosity upper limits for all novae from previous studies which
are not detected anymore and for all CNe in our field of view with optical
outbursts between May 2005 and March 2007. We detected eight X-ray counterparts
of CNe in M 31, four of which were not previously known. Seven sources can be
classified as SSSs, one is a candidate SSS. Two SSSs are still visible more
than nine years after the nova outburst, whereas two other nova counterparts
show a short SSS phase of less than 150 days. Of the latter sources, M31N
2006-04a exhibits a short-time variable X-ray light curve with an apparent
period of (1.6+-0.3) h. This periodicity could indicate the binary period of
the system. From the 14 SSS nova counterparts known from previous studies, ten
are not detected anymore. Additionally, we found four SSSs in our XMM-Newton
data without a nova counterpart, one of which is a new source. Out of eleven
SSSs detected in our monitoring, seven are counterparts of CNe. We therefore
confirm the earlier finding that CNe are the major class of SSSs in the central
region of M 31. We use the measured SSS turn-on and turn-off times to estimate
the mass ejected in the nova outburst and the mass burned on the white dwarf.
Classical novae with short SSS phases seem to be an important contributor to
the overall population.
