The forthcoming Deuterium-Tritium (DT) campaign at the Joint European Torus (JET) will induce a significant activation of the system components. In the present work we evaluate the temporal evolution of the radioactive species in the main in-vessel components after the end of the future DT campaign, assuming different levels of neutron irradiation. The neutron flux in the selected components is calculated by the MCNP5 code using the emission source by a typical DT plasma. The resulting neutron spectra are then input to the FISPACT code that computes the evolution of the radioactive species generated by the neutron activation process. For each irradiation scenario, the time behavior of the contact dose rate is determined.