Raster image cross-correlation spectroscopy (ccRICS) can be used to quantify the interaction affinities between diffusing molecules by analyzing the fluctuations between two-color confocal images. Spectral crosstalk compromises the quantitative analysis of ccRICS experiments, limiting multicolor implementations to dyes with well-separated emission spectra. Here, we remove this restriction by introducing raster spectral image correlation spectroscopy (RSICS), which employs statistical filtering based on spectral information to quantitatively separate signals of fluorophores during spatial correlation analysis. We investigate the performance of RSICS by testing how different levels of spectral overlap or different relative signal intensities affect the correlation function and analyze the influence of statistical filter quality. We apply RSICS in vitro to resolve dyes with very similar emission spectra, and carry out RSICS in live cells to simultaneously analyze the diffusion of molecules carrying three different fluorescent protein labels (eGFP, Venus and mCherry). Finally, we successfully apply statistical weighting to data that was recorded with only a single detection channel per fluorophore, highlighting the general applicability of this method to data acquired with any type of multicolor detection. In conclusion, RSICS enables artifact-free quantitative analysis of concentrations, mobility and interactions of multiple species labeled with different fluorophores. It can be performed on commercial laser scanning microscopes, and the algorithm can be easily extended to other image correlation methods. Thus, RSICS opens the door to quantitative multicolor fluctuation analyses of complex (bio-) molecular systems.