Optical transmission measurements have been made on thin high quality crystals of GaSe in fields of up to 93.5 kG. The fields were aligned parallel and perpendicular to the ψ axis. The symmetries of the valence and conduction bands are discussed in the light of the zero field data, and subsequently the behavior of the excitons in the magnetic field is discussed. Values for the effective masses of holes and electrons normal to the ψ axis are determined to be 0.45m0 and 0.20m0 respectively. The values of the g factors parallel and perpendicular to the ψ axis are also deduced.