  We report on measurements of the adiabatic second order elastic constants of
the off-stoichiometric Ni$_{54}$Mn$_{23}$Al$_{23}$ single crystalline Heusler
alloy. The variation in the temperature dependence of the elastic constants has
been investigated across the magnetic transition and over a broad temperature
range. Anomalies in the temperature behaviour of the elastic constants have
been found in the vicinity of the magnetic phase transition. Measurements under
applied magnetic field, both isothermal and variable temperature, show that the
value of the elastic constants depends on magnetic order, thus giving evidence
for magnetoelastic coupling in this alloy system.
