We investigate the influence of quantum-kinetic effects on the linear optical properties of semiconductors near the band edge. These effects arise from a non-Markovian treatment of the scattering terms in the semiconductor Bloch equations and result in a strong dependence of many-body effects on the energy. We compare with results using a Markovian approximation of scattering, where the many-body effects do not depend on energy and correspond to those in a quasi-particle approximation. We demonstrate, that within such a treatment both linewidth and shift of the exciton are strongly overestimated. Finally, the Mott density of excitons differs by a factor of two. The importance of the quantum-kinetic approach for the explanation of polariton-pulse propagation experiments is shown.1 Introduction Ultra-short laser pulses in the order of a few femto-seconds have opened the possibility to study the temporal evolution of many-body effects in a laser excited semiconductor. This includes as well the generation and dephasing of the laser induced coherent polarization and the formation of carriers populations and their relaxation into quasi-equilibrium. A new concept for the theoretical description of the coupled kinetics of coherent polarization and carriers had to be developed in order to explain the experimental findings. The main point in this quantum-kinetic description (for a review see [1][2][3]) is the non-Markovian treatment of scattering between carriers, polarization and elementary excitations, as plasmons and phonons. Evidence for quantum-kinetic effects both in Coulomb and LO-phonon scattering was found in several experiments, investigating the decay of the four-wave mixing signal [4][5][6].However, these time resolved investigations give no spectral information and cannot be performed for lower excitations, where excitonic effects become important, in particular the limit of linear response cannot be achieved. In this paper we focus on this limit. We consider a pump-probe experiment, where carriers are pumped and relaxed into quasi-equilibrium, and the optical response is detected by a weak probe pulse. We demonstrate, that (i) quantum-kinetic effects in the scattering of the probe-induced polarization with the elementary excitations (plasmons, LO-phonons) in the electron-hole plasma play an important role, even at lowest excitations, and (ii) give new insight and better understanding of these many-body effects from the viewpoint of Green's function description for the excited semiconductor.