  It is widely accepted that quite a number of double compact objects (DCOs) in
the Milky Way can be identified by future space-based gravitational wave (GW)
detectors, while systematic investigations on the detection of the GW sources
in nearby galaxies are still lacking. In this paper, we present calculations of
potential populations of GW sources for all types of DCOs in the Local Group
galaxy M31. For M31, we use an age-dependent model for the evolution of the
metallicity and the star-formation rate. By varying assumptions of
common-envelope ejection efficiencies and supernova-explosion mechanisms during
binary evolution, we make predictions on the properties of DCOs that can be
detected by the Laser Interferometer Space Antenna (LISA). Our calculations
indicate that a few (a dozen) DCOs are likely to be observed by LISA during its
4 (10) yr mission. We expect that the sources with black-hole components are
more likely to be firstly identified during a 4-yr mission since these binaries
have relatively large chirp masses, while the systems with white-dwarf
components dominate the overall population of detectable GW sources during a
10-yr mission. LISA can only detect very tight fast-merging systems in M31,
corresponding to the peak of orbital period distribution from $\sim 2$ min for
double white dwarfs to $\sim 20$~min for double black holes.
