  Ferromagnetic \nmg has unique magnetoelastic properties. These are
investigated by detailed computational studies of the phonon dispersion curves
for the non-modulated cubic \Ltw and tetragonal structures. For the \Ltw\
structure, a complete softening of the transverse acoustic mode has been found
around the wave vector $\mathbf{q}=[1/3,1/3,0](2 \pi/a)$. The softening of this
\TA{2} phonon mode leads to the premartensitic modulated super-structure
observed experimentally. Further phonon anomalies, related to other structural
transformations in \nmg, have also been found and examined. These anomalies
appear to be due to the coupling of particular acoustic phonon modes and
optical modes derived from Ni.
