A two-dimensional immune algorithm is proposed for resolving the multicomponent overlapping two-way data matrices. The method is a development of the one-dimensional immune algorithm proposed elsewhere. When the inner product of vectors is expanded to the similar operation on matrices, the 1D immune algorithm can be expanded to the 2D algorithm which is suitable for the analysis of two-way data matrices. Both simulated and experimental two-way data sets were investigated by the method, and the results prove that the 2D immune algorithm is an effective tool for resolving the overlapping two-way signals. The effect of noise on the recoveries is also discussed.