Uniaxial stretching and swelling are considered as two limiting cases of deformations of elastomers. Under both conditions, the molecular dynamics is changed with respect to the behavior that describes the undisturbed, equilibrium elastomer. Particularly the spectrum of segmental motions, which reveals itself in the frequency-dependence of the longitudinal NMR relaxation time, is discussed in this study, but also order effects expressed via the dipolar coupling strength are investigated. For stretched elastomers, a significant change of the relaxation dispersion is found for three different types of rubber; it is a consequence of a change of the mode spectrum of segmental motions that becomes obvious at low frequencies (below 1 MHz at room temperature). In swollen elastomers, on the other hand, a cross-over towards a behavior expected for semi-dilute solutions is found, and a comparison to solutions of uncross-linked polymers reveals a significant effect of the cross-links only in the kHz range. A much more pronounced difference between elastomers and polymer solutions, however, is found from double--quantum encoded NMR measurements where the residual order introduced by the presence of permanent cross-links is maintained even in the presence of solvent.