A generalization of the main linear and nonlinear correlation methods, the dual nonlinear correlation (DNC), is introduced. Various filters (CMF, POF, IF, FPF, PPC, OF) appear to be special cases of the DNC. The convolution formula describing the peak shape and the intermodulation effects for the noise-free multi-object scenes is discussed. Optimization of the DNC according to the peak-to-correlation energy criterion is performed. Superior performance of the PPC is presented. The influence of noise on the intermodulation effects is studied. Hybrid, optoelectronic realization of the DNC based on joint transform correlator architecture with nonlinear preprocessing which allows the introduction of various correlation methods without any fiters is proposed.