In this paper we consider the adiabatic transfer in three-level systems using the counterintuitive pulse sequence, the stimulated Raman process (STIRAP). We consider explicitly the nonadiabatic corrections to the ideal case. The problem simplifies when we use certain pulse types extending to infinity, ramp pulses. In this case we find models which are analytically solvable. In the smooth pulse case, we find simple exponential corrections to adiabatic behavior. For a resonant intermediate level, the problem is equivalent to a two-level problem, where adiabatic corrections have been investigated extensively. We utilize these results to interpret the behavior of the three-level system exposed to the counterintuitive pulse case. When the pulse separation is in a certain range, exponential adiabatic behavior is found, and the numerical data can be explained by the analytic theory taken from the two-level work. We cannot explain all results analytically, but the computations suggest that this description of the three-level system gives a good understanding of the STIRAP. \textcopyright{} 1996 The American Physical Society.