Fluorescence correlation spectroscopy (FCS) is a well-established method for the analysis of freely diffusing fluorescent particles in solution. In a two-colour setup, simultaneous detection of two different dyes allows the acquisition of both the autocorrelation of the signal of each channel and the cross-correlation of the two channels (fluorescence cross-correlation spectroscopy, FCCS). The cross-correlation function is related to the amount of diffusing particles carrying both dyes and can be used for monitoring a binding reaction. Here we develop a formalism for a quantitative analysis of ligand binding from a combination of the auto- and the cross-correlation amplitudes. Technical constraints, like the focal geometry, background signal and cross-talk between the detection channels as well as photophysical and biochemical effects which modulate the brightness of the particles are included in the analysis. Based on this framework a comprehensive treatment for the determination of two-component bind