Abstract The critical level behaviour of internal Alfen-gravity waves in a perfectly conducting shear flow in the presence of an aligned magnetic field is re-examined. A new form of the governing wave equation is given which has only two singularities Ω d = ±Ω A , where Ω d is the Doppler-shifted frequency and Ω A is the Alfven frequency. (Previously a form with three singularities has been used.) When the shear flow profile is linear, hydromagnetic waves propagating across the critical levels are attenuated at the hydromagnetic critical levels Ω d = ±Ω A . As the wave approaches the first critical level, the wave momentum decreases by a factor of exp(-2μ0π)[1 +coth(μ0π)]; as it approaches the second there is a further decrease by a factor [1+coth(μ0π)]−1, where μ0= (J H −¼)½. and J H is the hydrodynamic Richardson number. Unlike in the work of Rudraiah and Venkatachalappa (1972) where two gross attenuation factors are obtained, this yields just one gross attenuation factor exp(-2μ0π). These results are a...