The pulsed EPR (electron paramagnetic resonance) spectra and spin relaxation measurements of eight North American premium coal samples, prepared by the Argonne National Laboratory, have been examined. A method is presented for separating the parts of the EPR spectrum from the inertinite macerals from the spectra of the other macerals which is based on the FID (free induction decay) and the field dependence of the spin echo intensity. The mineral matter spins do not appear in these spectra. Good inertinite spectra can be obtained by this method but obtaining non-inertinite spectra that are simultaneously free of power and uncertainty broadening and free of instantaneous diffusion artifacts is difficult to achieve. The numbers of free radicals per gram of inertinite were determined from the FID by comparison with the FID of a standard TEMPO sample, except for those cases in which the FID may be too short to appear beyond the instrument deadtime. The numbers of spins in the inertinite lines are higher and appear to be more reasonable measurements than those reported from CW EPR. The numbers of free radicals per gram in the non-inertinite macerals were determined from the field dependence of a three-pulse echo in comparison with a coal tar pitch standard sample. It is shown that, unless the inhomogeneities that are shown to exist in the instantaneous diffusion rates from one field to another in the broad, non-inertinite lines are explicitly accounted for, the numbers of spins in high spin concentration samples are likely to be overestimated. The spin-spin relaxation times T2 of the broad line macerals were determined from plots of the two-pulse echo decay times in the limit of low pulse turning angle. The non-inertinite T2(-1) increase approximately linearly with the numbers of spins per gram, consistent with a dipolar spin-diffusion mechanism. The spin-spin relaxation mechanism in the inertinites appears to be due to spin exchange, which results in homogeneous line narrowing and increasing T2(-1) with increasing number of spins. The spin-lattice relaxation times T1 of the broad and narrow line spectra were measured respectively by echo saturation and by FID inversion recovery methods. The spin-lattice relaxation times in all macerals were found to decrease generally with increasing carbon content and decreasing hydrogen content. Previous work suggested a mechanism in which the proton hyperfine interaction is modulated by the lattice. T1(-1) is proposed as an index of coal matrix flexing. Observations of broad-line coal echo spectra at various degrees of instantaneous diffusion decay reveal significantly g-shifted broad-line spectra whose shifts correlate with the oxygen and sulfur content of the coal.