The classical tube-reptation (TR) model is based on the assumption, that in entangled polymer melts diffusion takes place inside the effective tubes having a conformation of ideal chains and being stable on the time scale of the terminal relaxation time tt, the latter being strongly molar mass (M) dependent. We argue, that this assumption leads for high M to a characteristic, strongly non-exponential time dependence of the deuteron Free Induction Decay, or likewise of the Hahn Echo amplitude. This holds for times t satisfying the condition tau(e) << T-2 < t << tau(t) where T-2 is an effective spin-spin relaxation time and tau(e) is the entanglement time. (C) 2018 Elsevier Ltd. All rights reserved.