Exciton-quasiparticle interactions govern the optical nonlinear response of heretostructures at the exciton transitions. We theoretically analyze the exciton-exciton, exciton-electron, and exciton-hole interactions in heterostructures with GaAs/AlGaAs quantum wells (QWs), however, our theoretical approach can be applied to other types of heterostructures. The exciton-quasiparticle scattering amplitudes are calculated in the framework of the two-particle Hartree-Fock approximation. The exchange interaction, which is mainly responsible for the scattering, is modeled using microscopically calculated exciton wave functions. The corresponding exchange interaction constants are determined as a function of quantum well width. The spin-dependent exciton-quasiparticle elastic scattering matrix elements are used to obtain the collisional broadening of the exciton transition within the Born approximation as a function of the areal density of the respective quasiparticles for QWs of various widths. The obtained density dependences of the collisional nonradiative broadening can be used to estimate the exciton and charge carrier densities in optical experiments.