There is considerable, and growing, interest in the 64Cu radioisotope for application in Nuclear Medicine for PET imaging and targeted radiotherapy of tumours. We are investigating the cyclotron production of this isotope by way of deuteron bombardment of enriched 64Zn target material. In this study, experimental excitation functions for both the 64Zn(d,2p)64Cu and 64Zn(d,alphan)61Cu reactions up to 18.2 MeV deuteron energy have been measured using the stacked-foil technique. The deuteron energies in the various foils were calculated with the SRIM 2003 code and gamma-ray spectrometry was used to measure the activities of the various radioisotopes produced. Monitor foils were used to determine the deuteron beam current on the target stack. Theoretical excitation functions, calculated both with the Empire II code and with an updated version of the Alice code, were compared with the experimental results and a reasonable agreement was found. The experimental work was performed at the MC40 Cyclotron at the European Commission's Joint Research Centre at Ispra, Italy.