The dynamics of polyisobutylene at 407 K is investigated by means of quasi-elastic neutron scattering. By proper data reduction, data from two different instruments were combined to provide the incoherent intermediate scattering function, I-s(Q,t), over 3 decades in time. The data were interpreted in terms of a superposition of exponentials with a distribution of characteristic times. The data provide an indication of the existence of three different relaxation processes in the time range between 0.1 and 1000 ps, thus confirming recent results from molecular dynamics simulations. The two fastest processes are spatially localized, while the slow one shows a momentum transfer dependence. Analysis in terms of the alternative phenomenological approach of stretched exponential is also discussed.