Entropy production in the compression stage of heavy ion collisions is discussed within three distinct macroscopic models (i.e. generalized RHTA, geometrical overlap model and three-fluid hydrodynamics). We find that within these models ~80% or more of the experimentally observed final-state entropy is created in the early stage. It is thus likely followed by a nearly isentropic expansion. We employ an equation of state with a first-order phase transition. For low net baryon density, the entropy density exhibits a jump at the phase boundary. However, the excitation function of the specific entropy per net baryon, S/A, does not reflect this jump. This is due to the fact that for final states (of the compression) in the mixed phase, the baryon density pR increases with v G, but not the temperature T. Calculations within the three-fluid model show that a large fraction of the entropy is produced by nuclear shock waves in the projectile and target. With increasing beam energy, this fraction of S/A decreases. At ~ = 20 A GeV it is on the order of the entropy of the newly produced particles around midrapidity. Hadron ratios are calculated for the entropy values produced initially at beam energies from 2 to 200 A GeV. (~) 1998 Elsevier Science B.V.