Deuterium solid-state echo delay line shapes are used to establish the local motions occurring in linear and cross-linked epoxy systems based on Bisphenol A. Four isotopically labeled samples were prepared : linear and cross-linked resins with deuterated methylene units, and linear and cross-linked resins with deuterated phenylene units. Two local motions are observed in all four samples : trans-gauche isomerization of the methylene units and pi flips of the phenylene units. The solid-state echo delay line shapes were simulated to obtain the rates of motion, the amplitudes of motion, and apparent distribution of rates, and the apparent temperature dependence of the rates. The two jump motions differ by about an order of magnitude in rate, with the JE flip process being the faster of the two. Both have similar distributions of relaxation times given by a stretched exponential correlation function with an exponent of 0.6-0.7. The apparent activation energy for the pi flip process is 50 kJ/mol and for the trans-gauche isomerization, 57 kJ/mol. For a given frequency, the breadth and temperature of the shear loss peak can be calculated from the information determined from the NMR data. Both motional processes lie in the envelope of relaxation referred to as the beta process, with the pi flips occurring on the lower temperature side of the envelope and the trans-gauche isomerization occurring on the higher temperature side. These two motions do not appear to account for all of the relaxations contributing to the beta peak.