In several cellular systems, the phasor FLIM approach has shown the existence of more than 2 components in the same pixel, a typical example being free and bound NADH. In order to properly quantify the concentrations and the spatial distributions of fluorescence components associated with different molecular species we developed a general method to resolve 3 and 4 components in the same pixel using the phasor approach. The method is based on the law of linear combination of components valid after transformation of the decay curves to phasors for each pixel in the image. In principle, the linear combination rule is valid for an arbitrary number of components. For 3 components we use only the phasor position for the first harmonic, which has a small error, while for 4 components we need the phasor location at higher harmonics that have intrinsically more noise. As a result of the noise in the higher harmonics, caused by limited photon statistics, we are able to use linear algebra to resolve 4 components given the position of the phasors of 4 independent components in mixtures of dyes and 3 components for dyes in cellular systems.