The level scheme of⁷⁹Kr has been studied through the⁷⁹Br(p,n)⁷⁹Kr reaction at proton energies from 1·7 to 5·0 MeV.γ-ray and internal conversion electron measurements were made using Ge(Li) detectors and a six gap “Orange” electron spectrometer. The level scheme was established by determining the thresholds of variousγ-rays and byγ-γ and n-γ coincidence measurements. New levels at 402, 450, 660, 676, 695, 720, 810, 836, 907 and 1038 keV not observed in earlier radioactivity studies have been established. DefiniteJ^π assignments have been made to most of the levels below 800 keV. Many of the low-lying levels are identified as rotational levels based on the (301 ↓) 1/2⁻, (301 ↑) 3/2⁻ and (431 ↓) 1/2⁺ Nilsson states.