The growth of waves along the direction of motion of viscous compressible liquid sheets in inviscid compressible gas streams was investigated. Gas streams were considered to move at different velocities relative to the liquid sheet. A dispersion relation was derived for the spatial growth of longitudinal waves in the presence of lateral wave modes. The solution of the dispersion relation showed that the incorporation of gas compressibility increases the growth of paraantisymmetric waves. Compressibility in liquid, such as obtained by the dispersion of gas bubbles, has a much lower influence on the growth of paraantisymmetric waves. The presence of lateral wave modes did not influence longitudinal wave growth when the compressibility of liquid and gas was considered in the model. © 2010 The Japan Society of Fluid Mechanics and IOP Publishing Ltd.