Multilayer growth using phenomenological rate equations is studied. These equations are developed from those for one-monolayer growth. The basic phenomena include the flux of atoms, desorption, and adsorption of a single adatom and incorporation of adatoms with other adatoms or with a stable cluster. In addition, we investigate the effect of migration of adatoms between layers. The same measures for growth modes are used as in our earlier Monte Carlo studies. These two approaches give consistent results. We conclude that the static and kinetic approaches to determine growth modes differ substantially.