Nuclear Magnetic Resonance (NMR) is a widely used tool in functional and structural genomics for the study of three-dimensional structures of proteins. The experimental data obtained by this method are multidimensional spectra consisting of about 10⁷ data points. We demonstrate that Three Way Decomposition (TWD) provides an inherently suitable tool for the analysis of these spectra. We apply here TWD for the first time to a NOESY-NOESY spectrum, which in terms of number of signals is among the most complex spectra. The application shows that the three-dimensional NMR spectra can be faithfully described by the components resulting from TWD, yielding among other advantages a data compression factor of over 100. The inherent relation between NMR and TWD is demonstrated on the NOESY-NOESY spectrum by deducing the TWD model from the mathematical description of the NMR experiment. Applicability of TWD to various types of NMR spectra, the use of sparse experimental data sets in order to reduce instrument time and other aspects of the analysis are discussed.