It is a challenge to recognize faces under variable poses or illumination directions. In the area of multiview face recognition, many experimental results have shown that the performance of approaches based on multiple eigenspaces is higher than the performance of those based on a single eigenspace. This paper presents two multiple illumination eigenspaces-based methods, RDEB and BPNNB, for solving the variable illumination problem of face recognition. The experiment shows that the methods have a high recognition ratio. In particular, BPNNB has outperformed the assumptive method which knows the illumination directions of faces and completes recognition in the specific eigenspace using eigenface method[2] for each face subset with a specific illumination direction