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Summary form only given.The coherent response of excitons in semiconductor nanostructures, as measured in four wave mixing (FWM) experiments, depends strongly on the inhomogeneous broadening of the exciton transition. We investigate GaAs-AlGaAs single quantum wells (SQW) of 4 nm to 25 nm well width. Two main mechanisms are found to be important. First, the excitation-induced dephasing FWM signal (EID), which leads to a strong dependence of the signal on the angle between the linear input polarizations. The presence of the EID in the mainly homogeneously broadened sample (25 nm) is shown by the beating between EID and two-photon coherence (TPC) at the exciton for negative delay and co-linear polarized excitation. It vanishes for cross-polarized excitation, thus excluding the importance of local-field effects.