The exact pulse solution of Brewer and Hahn (1975) for the two-photon resonance of the three-level atom uses light pulses of distinct frequencies that are applied nonadiabatically with respect to the frequency offset ? of the intermediate atomic state. The adiabatic two-photon vector model of Grischkowsky et al. (1975), considers light adiabatically applied with respect to ?, and hence the high-frequency ringing terms are absent. The Brewer and Hahn model is identical with the vector model in the adiabatic limit, as ? is increased arbitrarily. However, each approach has its special areas of application where the other is inappropriate Abstract Numbers: A1977-057957