The properties and resonant absorption mechanism of the Alfv¿n compressional waves are discussed for a cold plasma. The parametric analysis of the dispersion equation shows that unlike the incompressible case the excitation of the compressional surface waves near the resonant surface depends on the specific vlaues of the plasma parameter across this surface. The oscillation frequency and the resonant absorption coefficient of these waves also show a different behavior from those of Alfv¿n waves. The phase velocity &ohgr;/k∥ depends on the perpendicular wave number k⊥, and the absorption coefficient is proportional to (Ka)2/3, where K=(k2∥+k⊥)1/2 and 2a is the scale length of the density variation. ¿ American Geophysical Union 1989