Two-dimensional electron paramagnetic resonance (BD-EPR) spectra of Illinois No. 6 and Upper Freeport coals have been measured. From 2D-nutation spectroscopy, it is confirmed that the main EPR signal around g = 2 is attributed to free radicals, but not to radical pairs. Both coals showed nuclear modulation effects due to H-1 and naturally abundant C-13 nuclear spins. Spin-echo correlation spectroscopy (SECSY) experiments elucidate the distribution of modulation frequencies included in a broad EPR spectrum. The observed dip in the C-13 matrix spectrum obtained from SECSY is interpreted in terms of the decrease of vitrinite radicals, which are weakly interacting with C-13 nuclei, in the central region of the EPR spectrum. The analysis of the broad hyperfine spectra due to H-1 and C-13 nuclei in the hyperfine sublevel correlation spect-ra suggests the existence of several kinds of radicals in coal. Most of unpaired electrons are considered to be trapped in aromatic rings. The ratio of C-13/H-1 of hyperfine spectra increases with coal rank, suggesting a new index of coal rank.