The frequency dependence of the proton spin-lattice relaxation times T1 and T1., in the laboratory and rotating frames, respectively, is reported for solid and liquid phases of poly(diethylsiloxane) (PDES) and in melts of poly(dimethylsiloxane) (PDMS). The total frequency range is 5 X 102 -3 X 108 Hz and is mainly covered by field-cycling NMR relaxation spectroscopy. The relaxation behavior of PDES in the liquid but ordered mesophase is compared to that of isotropic melts of PDES and PDMS and also to that of nematic main-chain liquid-crystal polymers. The frequency dependences of PDES and PDMS liquids can be represented at low and high frequencies by power laws, section by section. The relaxation behavior in the isotropic melts is entirely equivalent to that previously reported for other polymer species. In the PDES mesophase, the exponents of the power laws are significantly larger and the crossover frequency between the two regimes is reduced. The dynamics in this phase are discussed with respect to the influence of chain modes and order director fluctuations. The main conclusion is, on the whole, that data of the liquid phases are determined by chain modes rather than by local segment fluctuations. The chain dynamics in the PDES mesophase resemble the chain modes in isotropic melts modified for a microstructure with reduced randomness, whereas the influence of order director fluctuations can neither be confirmed nor ruled out.