The evolutions of the spectrum and spatial-coherence of light in optical resonators are investigated theoretically in detail on the basis of coherence theory in the space-frequency domain. The initial light in the resonator is assumed to be polychromatic and spatially incoherent with a certain spectral width. By considering the effects of the edge diffraction and phase modulation, the evolutions of the spectrum and coherence are clearly demonstrated for different types of resonator. The results show that the spectral evolution is affected not only by the g-factor of the resonator (the type of resonator), but also by the edge diffraction and phase modulation. We introduce a new parameter, called the global degree of spatial coherence, to characterize the spatial coherence on each mirror. The spatial-coherence evolution is also affected by g-factor of the resonator, edge diffraction, and phase modulation. The physical mechanism of these phenomena is explained and discussed.