Diffraction gratings are key components in many applications including pulse compression and stretch, optical imaging, spectral encoding and decoding and optical filtering. In this paper, spatial dispersion of two typical diffraction grating-based optical systems, single-grating system and grating-pair system, are thoroughly studied. The single-grating system consists of a diffraction grating to disperse the quasi-monochromatic lights and a convex lens to make the lights propagate in parallel and focused. In the grating-pair system, a pair of diffraction gratings is used to disperse the collimated lights in parallel. The spatial dispersion law for the two systems is developed and summarized. By investigating the spatial dispersion, the two systems are compared and discussed in detail.