The propagation of transient waves is considered along the principal axis of symmetry in a magnetic crystal. The occurrence of magnetoelectric effects, characterized by skew-symmetric susceptibilities, gives rise to wave modes propagating in opposite directions with different speeds and different amplitude attenuation. The wave propagators are evaluated for each mode through an asymptotic expansion of the Laplace transforms of the constitutive functions. Thermodynamic restrictions on these functions are shown to impose wave damping due to time dispersion and to the presence of electric conductivity. Reflectivity at a discontinuity surface within the magnetic material is also investigated in detail. Dissipative effects are shown to characterize the behaviour of the reflected field.