The present paper describes a new experimental scheme for following diffusion and chemical reaction systems of fluorescently labeled molecules in the nanomolar concentration range by fluorescence correlation analysis. In the dual-color fluorescence cross-correlation spectroscopy provided here, the concentration and diffusion characteristics of two fluorescent species in solution as well as their reaction product can be followed in parallel. By using two differently labeled reaction partners, the selectivity to investigate the temporal evolution of reaction product is significantly increased compared to ordinary one-color fluorescence autocorrelation systems. Here we develop the theoretical and experimental basis for carrying out measurements in a confocal dual-beam fluorescence correlation spectroscopy setup and discuss conditions that are favorable for cross-correlation analysis. The measurement principle is explained for carrying out DNA-DNA renaturation kinetics with two differently labeled complementary strands. The concentration of the reaction product can be directly determined from the cross-correlation amplitude.