We propose and investigate the magnetoelastodynamic mechanism of the wave m
otions of poorly ionized superparamagnetic gas-dust interstellar medium cap
able of sustaining long-ranged magnetization. It is suggested that the mole
cular linewidths inferred from recent Zeeman measurements of the magnetic f
ield toward the core position in dark interstellar molecular clouds may be
due to transverse magnetomechanical waves traveling with supersonic, but su
b-Alfvenic, speed.