The interdependence between the temporal and the longitudinal and transverse spatial coherence is analyzed. The analysis concerns both the derivation of the exact analytical propagation equation of the mutual coherence in free space from a planar and spherical boundary surface and the numerical analysis of a specific model. This model assumes the mutual coherence function to be spatially incoherent at a planar surface. The temporal coherence of the mutual coherence function on the planar or spherical boundary surface is not quasi-monochromatic but much more general and given by Eq. (41). Two theorems are derived that are a generalization of the van Cittert-Zernike theorem.