The multirate processing of two-dimensional (2D) signals involves various types of sampling and matrices, due to different grid geometry. A more consistent theory is then needed in order to obtain better techniques and useful results in many areas, such as image and signal processing, biomedical, telecommunications, multimedia, remote sensing, optics. In this work, a 2-channel complementary filter banks theory, designed based on 2D multirate processing and complementary filters properties is presented with foundations for multiresolution levels methods modeling, for the processing of signals in two-dimensions, in nonseparable way. Signal analysis and synthesis using 2-channel complementary filter (CF) banks, the conditions under which the reconstruction of the 2D input signal is perfect and frequency division in the analysis part are developed. Since multiresolution decomposition of signals, wavelet representation and filter banks have a strong link, a relation of then with complementary filter banks is done. Other multiresolution levels methods can be derived from this theory and applications of them were found for compression, edge detection, 2D scaling and wavelets functions and digital TV systems.