Field-cycling and field-gradient H-1 NMR experiments were combined to reveal the segmental mean-square displacement as a function of time for polydimethylsiloxane (PDMS) and polybutadiene (PB). Together, more than 10 decades in time are covered, and all four power-law regimes of the tube-reptation (TR) model are identified with exponents rather close to the predicted ones. Characteristic polymer properties like the tube diameter a(0), the Kuhn length b, the mean-square end-to-end distance < R-0(2)>, the segmental correlation time tau(s)(T), the entanglement time tau(e)(T), and the disengagement time tau(d)(T) are estimated from the measurements and compared to results from literature. Concerning tau(d)(T), fair agreement is found. In the case of tau(e), agreement with rheological data is achieved when the time constant is extracted from the minimum in the shear modulus G ''(omega). Concerning the TR predictions the molar mass (M) dependence of tau(d) is essentially reproduced. Yet, calculating tau(e) from tau(d) for PDMS yields agreement with experimental data while for PB it gets by 2 orders of magnitude too short. In no case tau(e) is correctly reproduced from tau(s)(T). Segmental and shortest Rouse times appear to coincide for PB, while in the case of PDMS the latter turns out to be longer by 1 decade.