The kinetics of nucleation and growth of helium bubbles in alpha-irradiated copper have been investigated by isothermal positron lifetime studies. Helium has been homogeneously implanted in pure copper samples using alpha particles from a cyclotron to a concentration of 100 appm. Postimplantation positron lifetime studies have been carried out in the bubble nucleation stage at isothermal annealing temperatures of 500, 520, and 550 K. The mean positron lifetime, τ, shows a decrease as annealing time is increased, and the rate of decrease of τ is faster for higher annealing temperatures. These changes in τ indicate that the rate-controlling mechanism for bubble nucleation is thermally activated migration of helium to the nucleating site. The activation energy for helium migration, EMHe, has been determined from an analysis of these isothermal curves employing the cross-cut method. The deduced value for EMHe is found to be 1.36 ± 0.15 eV. This supports helium migration by an impeded interstitial migration mechanism, otherwise known as the dissociative mechanism, for which the activation energy in Cu is estimated to be in the range 1.20 to 1.49 eV. Isothermal positron lifetime measurements have also been carried out in the bubble growth regime at annealing temperatures of 720, 750, and 775 K. An analysis of the isothermal variation of the mean lifetime, τ, similar to the above, yields an activation energy for the bubble growth as EG = 2.4 ± 0.3 eV. This suggests that the Ostwald ripening process is responsible for the helium bubble growth in copper.