The effect of compressibility on the propagation and resistive dissipation properties of magnetohydrodynamic waves in nonuniform media is studied by using a normal mode analysis. We concentrate on wave models for which the resistivity acts over the entire system, thus excluding localized resonant absorption. We identify the wave modes in nonhomogeneous situations in term of their familiar homogeneous counterparts and show that only the shear Alfven and slow magnetosonic modes survive in the resistive regime. The most promising heating agents in the astrophysical context are shown to be the shear Alfven waves that behave almost incompressibly.