In this paper we detail the dynamics of intrinsic excitons in the alloy CdxZn1-xTe/ZnTe quantum well system. Both single and multiple quantum well structures are studied. The strength of the thermal broadening of the exciton is measured up to room temperature and is found to be well-width and composition dependent. We also observe non-resonant fluorescence line narrowing in these materials which leads to sharp lines sitting on top of inhomogeneously broadened exciton luminescence at low temperature. Using both lifetime and dephasing measurements these lines are found to be predominantly luminescence in nature. We measure the spectral diffusion of excitons within the inhomogeneously broadened line by time-resolved luminescence. The extent of the exciton localization can be deduced by a comparison of the dephasing and spectral diffusion times with other systems.