The variation of global coherence on propagation plane by plane is examined in the framework of coherent mode representation. It is explained through concrete examples that the global coherence may in general be enhanced, may be reduced, or may not change. When the mode functions form a complete set and the corresponding eigenvalues are in nitely degenerate, there necessarily develops a certain amount of global coherence on propagation, which is the essence of van Cittert-Zernike theorem. The propagation generates a certain pattern of the eigenvalue spectrum from the initial flat one and this is shown to be related to the non-unitarity of the propagation kernel.