Fluorescence Fluctuation Spectroscopy (FFS) studies the fluctuating fluorescent signal from a small illumination volume and extracts the concentration and dynamical information of fluorophores. Detecting the fluorescence in two detector channels introduces the possibility of differentiating the fluorophores based on color. We introduce bivariate cumulant analysis for Two-Color Fluorescence Fluctuation Spectroscopy and derive an analytical expression for the bivariate factorial cumulants of photon counts at arbitrary sampling times. Fits of the data to the analytical model determine the brightness of each channel, occupation number and diffusion time of each fluorescent species. The statistical accuracy of each cumulant is described by its variance, which we calculate by the moments-of-moments technique. The theory is experimentally verified using model dye system. We also performed first experiments in living cells, and develop a model that takes nonideal detector effects into account. This technique is useful for optimizing the spectroscopic separation of heterogeneous biological samples by FFS.