The incoherent intermediate scattering function S-inc(Q, t) of polybutadiene (PB) and polyisobutylene (PIB) is measured on the neutron backscattering instrument IN16 in the ns-time range and in a temperature and pressure range where the observed relaxation is ascribed to segmental relaxation. S-inc (Q, t) at atmospheric pressure P-atm, for PB at T = 300 K and for PIB at T = 368 K, shows a characteristic momentum transfer (Q) dependence, if fitted by a single stretched exponential relaxation process S-inc (Q, t) =A (Q) exp(-t/tau(KWW))(beta) with fixed beta = 0.45 for PB and beta = 0.55 for PIB. For both polymers the Q-dependence of the relaxation time tau(KWW)(Q) in the range 0.2 Angstrom(-1) < Q < 1.9 Angstrom(-1) is compatible with a crossover from a power law tau(KWW) (Q) similar to Q(-2/beta) at low Q to tau(KWW) (Q) similar to Q(-2) at high Q. Application of pressure results for both polymers in an extension of the Q(-2)-range towards lower Q. A variation of the molecular weight (390 < M-W < 73 000) for PIB does hardly influence this characteristic tau(Q)-dependence at T = 368 K. We conjecture to see at high Q-values the influence of local relaxations with possibly rotational diffusion character resulting in a tau(Q) similar to Q(-2) behaviour. For M-W < 4040 and 90 K below T-g we find relaxations at higher energy (0.1-1 meV) which we ascribe tentatively to end-of-chain motions. Furthermore, we show for PB the possibility to separate thermal and density effects onto S-inc (Q, t) by controlling pressure along different thermodynamic paths. (C) 2003 Elsevier Science B.V. All rights reserved.