The stability of a horizontally stratified, electrically conducting fluid permeated by a uniform magnetic field aligned with the motion is investigated. The resulting linear stability problem for the special case of constant density gradient and linear shear in an unbounded fluid is reduced to the study of a third order differential equation in time. In the absence of dissipation, the linear shear eventually causes hybrid Alfv#xE9;n-gravity waves to decay algebraically. The effect of the shear is to shorten the vertical length scale. So with the addition of even small diffusivity, dissipation is strongly stabilising and all modes eventually collapse exponentially, generally at a fast rate. The evolution from wave motion to exponential decay is examined for particular limiting cases. When the fluid is bounded by horizontal planes a nonlinear stability criterion is derived using the energy method.
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