For three high molecular weight samples of poly(dimethylsiloxane), pol
ybutadiene, and polyisoprene the self-diffusion for times smaller than
the reptation time T(rep) was investigated using field gradient NMR i
n the stray field of a cryomagnet. A time-dependent apparent self-diff
usion coefficient D(app) is observed with time exponents b of the powe
r law D(app) approximately t(b) between -0.57 and -0.73. These values
are at variance with the strict reptation picture and support more rec
ent theoretical concepts and computer simulations.