The presence of surfactants, ubiquitous at most °uid/liquid interfaces, has a pronounced e®ect on the surface tension, hence on the stress balance at the phase boundary: local variations of the capillary forces induce transport of momen- tum along the interface { so-called Marangoni e®ects. The mathematical model gov- erning the dynamics of such systems is studied for the case in which the surfactant is soluble in one of the adjacent bulk phases. This leads to the two-phase balances of mass and momentum, complemented by a species equation for both the interface and the relevant bulk phase. Within the model, the motions of the surfactant and of the adjacent bulk °uids are coupled by means of an interfacial momentum source term that represents Marangoni stresses. Employing Lp-maximal regularity we ob- tain well-posedness of this model for a certain initial con¯guration. The proof is based on recent Lp-theory for two-phase °ows without surfactant.