The propagation properties of hydromagnetic-inertial-gravity waves in a Boussinesq fluid are studied for two representative models. One model is characterised by horizontal rotation, magnetic field and flow, the magnetic field and flow being perpendicular and vertically sheared. In the other model both magnetic field and rotation are vertical and uniform but the flow is horizontal and latitudinally sheared. In a slowly varying shear, when the WKBJ approximation is applicable, the wave normal surfaces for different values of magnetic field and flow are used to construct the various types of ray trajectories. In a full wave treatment, in which variations in the basic state are taken into account, it is found that the total wave energy flux (or the wave action flux), 𝒜, in the direction of the shear is constant except at critical layers (i.e. singularities predicted by the WKBJ treatment), where it jumps from one constant value to another. The invariance of 𝒜 is used to show that MAC-waves can be over-reflected by a finite shear layer free of critical layers. By adopting the correct matching procedure across critical layers the influence of hydromagnetic critical layers on the reflexion of hydromagnetic-inertial-gravity waves by finite shear layers is investigated. It is found that such critical layers can facilitate over-reflexion by “emitting” energy flux.