In the last decade, the growth of computer systems and the improving of atmospheric physics algorithms have lead to a wider use of nonhydrostatic models, even for operational purposes (i.e. HIRLAM, MC2, MM5 and others). The influence of vertical accelerations may be important in topographically complex domains and, among these, the alpine region is one of the most important one. The variations of vertical component of the wind do not affect only dynamics, but the thermal and moisture distribution, which, again, has an influence on the wind characteristics and the occurrence and strenght of precipitations. The paper contains test runs made with CEM multiscale, fully compressible equations, nonhydrostatic model. Particularly, it analyses the difference of results, using grid mesh sizes of 40, 20, 10 and 5 km on a domain covering northern Italy and the nearby areas around Alps. In this region, the atmospheric behaviour might depend strongly on nonhydrostatic processes, such as mountain waves, penetrative convection and orographically-enhanced storms. The test runs have been made in both hydrostatic incompressible and nonhydrostatic compressible mode. Initial results were obtained by comparing hydrostatic versus nonhydrostatic simulations of idealized barotropic and baroclinic instabilities. They have shown that the solutions, in compressible mode runs, grow more slowly than their incompressible counterparts. A linear stability analysis has also shown that the growth rates, for both instabilities, decrease with compressibility. Simulations of barotropic and baroclinic instability in the nonhydrostatic compressible mode are nearly identical to those using the hydrostatic one, but it appears that the relatively slow growth continues well into the nonlinear regime. Real case-studies of mountain waves and penetrative convection have been considered. It has been evidenced that, for hydrostatic simulations, finer resolutions lead to stronger vertical motions associated with mountain waves. Moreover, with 10 and 5 km grid mesh sizes, the downstream tilt of the main wave in the hydrostatic case was much smaller than in the nonhydrostatic one. Penetrative convection, in hydrostatic simulations, was also less evidenced. Vertical structures of propagating plumes of vertical motion were stronger and fairly well organized in the nonhydrostatic mode runs.