Thin selenium films were prepared by cathodic deposition on aluminium foils. The Al-Se-Al sandwich stacks were used for measurement of the excitation functions of the 76Se(3He,2n)77Kr, 77Se(3He,3n)77Kr and natSe(3He,xn)77Kr reactions up to 3He-particle energy of 36 MeV. Excitation functions were also measured for the competing reactions 76Se(3H,3n)76Kr, 76Se(3He,pn)77Br, 76Se(3He,p2n)76Br, 76Se(3He,p3n)75Br, 76Se(3He, alpha)75Se, 77Se(3He,n)79Kr, 77Se(3He,4n)76Kr, 77Se(3He,pn)78Br, 77Se(3He,p2n)77Br, 77Se(3He,p3n)76Br, 77Se(3He, alpha n)75Se, natSe(3He,xn)79Kr and natSe(3He,xn)76Kr. Thick target yields were calculated for the formation of krypton and bromine isotopes in 3He-induced reactions on 76Se and 77Se and for krypton isotopes in reactions on natural selenium. The possibilities of production of 77Kr using 3He-particle induced reactions on 76Se, 77Se and natSe were investigated. From the viewpoint of yield and purity, for the production of 77Kr the reactions 76Se(3He,2n)77Kr and 77Se(3He,3n)77Kr were found to be very suitable, the former at low energies and the latter at relatively higher energies. In the case of 76Se(3He,2n)77Kr reaction, a target thickness corresponding to E3Hc = 25 leads to 15 MeV leads to a theoretical thick target yield of 7.5 mCi 77Kr/micro Ah; the 76Kr impurity at EOB amounts to 0.45%. In the case of 77Se(3He,3n)77Kr reaction, on the other hand, for a target thickness corresponding to E3Hc = 36 leads to 15 MeV the calculated thick target yield of 77Kr is 11.5 mCi/micro Ah and the levels of impurities 79Kr and 76Kr at EOB amount to 0.35 and 0.36% respectively.