The mechanisms of exciton coherence relaxation in GaAs quantum wells in the linear mode have been experimentally investigated. An experimental technique has been developed for measuring the total phase relaxation rate, rates of reversible and temperature-irreversible excitonic phase relaxation, and the radiative decay rate ΓR of excitonic polarization. The experimental values of ΓR for a quantum well of specified thickness, obtained for a series of samples, have a spread not larger than 15%. This accuracy made it possible to estimate the shape of the dependence of ΓR on the well thickness LZ . It is experimentally found that ΓR is temperature-independent up to 80 K.