The prospect of employing the stimulated Raman adiabatic Passage (STIRAP) technique under the influence of pure dephasing is explored. A general analysis of how decoherence influences the performance of STIRAP is provided. Starting from a general and fully quantum-mechanical system-bath Hamiltonian, we derive a quantum master equation (QME) that describes the reduced dynamics of a dissipative STIRAP system. The derivation is based on the standard assumptions of (1) weak system-bath coupling; (2) Markovity, in the sense that the relaxation times are long in comparison to the bath correlation time, tau(c); and (3) weak field-matter interaction, in the sense that the Rabi period of the driving laser fields, Omega(-1), is longer than tau(c). The dissipative term in this QME is the same as it would have been in the absence of the driving fields, because of the assumption of weak field-matter interaction. This type of uncontrollable dephasing is seen to diminish the efficiency of STIRAP, although the actual loss strongly depends on the specific dephasing mechanism. We also derive a more general QME, which is applicable to driving fields of arbitrary intensity. The dissipative term in the new QME is explicitly dependent on the driving fields, and therefore controllable. Intense fields are shown to effectively slow down the dephasing when Omegatau(c)>1, which suggests that it may be possible to use STIRAP in order to transfer population between the quantum states of a solute molecule embedded in a solvent. (C) 2003 American Institute of Physics.