Inelastic and elastic neutron scattering have been used to study a single crystal of the Ni54Mn23Al23 Heusler alloy over a broad temperature range. The paper reports the experimental determination of the low-lying phonon dispersion curves for this alloy system. We find that the frequencies of the TA2 modes are relatively low. This branch exhibits an anomaly (dip) at a wave numberξ0=1∕3≈0.33, which softens with decreasing temperature. Associated with this anomalous dip at ξ0, an elastic central peak scattering is also present. We have also observed satellites due to the magnetic ordering.