Magic angle spinning NMR technique is used to measure rotating-frame spin-lattice relaxation times, 13C T1, 13C T1r, and 1H T1r, of amorphous and cryst. regions of polyoxymethylene (I) and high- and low-d. polyethylene (II) [9002-88-4]. Cryst. 13C T1 for I and II is orders of magnitude longer than the amorphous counterpart due to the rigidity in the cryst. regions in general and a difference in motion amplitude for I in particular, whereas 13C T1r shows an opposite trend. In contrast to I, both II samples exhibit biexponential decays for amorphous and cryst. 13C T1r and amorphous 1H T1r. Two values for amorphous 13C and 1H T1r are interpreted as an indication of nonuniformity in the amorphous regions of II, while long amorphous 1H T1r and short amorphous 13C T1r components are ascribed to those chains partly in or close to cryst. phase. Two values for cryst. 13C T1r in II are attributed to the 2-step spin-spin relaxation. Side-group resonances are obsd. for both II samples, while Me and Bu groups in low-d. II have relaxation times almost identical to the corresponding amorphous main-chain CH2 group relaxation times. This is explained by the internal Me rotation and/or by the presence of Bu side group in amorphous regions of II.