The dynamics of resonantly excited 1s-HH excitons in GaAs single quantum wells is studied by picosecond transient reflection and photon echo. The energy relaxation and transport properties of the excitons are probed, making use of the surface electric field. At low exciton densities and 5 K, transport appears to be absent, and superradiant decay takes the place of free excitons with characteristic times ranging from 5 to 13 ps, depending on the well width. The polarization decay is governed by energy relaxation, and a coherence length is found for these free excitons of ϳ200 nm. Low in the exciton resonance, we measure a much slower radiative decay and smaller coherence lengths, due to localization. Here both radiative decay and pure dephasing contribute to the polarization dephasing rate. At higher exciton densities and temperature, transport is observed, induced by exciton-exciton and exciton-phonon collisions. For free excitons it is demonstrated that the increased polarization dephasing rate is exclusively due to exciton transport, and not to pure dephasing. For localized excitons, pure dephasing processes prevail in T 2 , and thermally activated transport is found. ͓S0163-1829͑97͒05847-5͔