A co-rotating scroll machine operable as compressor or expander, comprises a transmission and guidance mechanism (9,10) for first and second scroll plates (7,8), having three transmission and guidance units (9,10) uniformly distributed around the scroll plates towards the periphery thereof. Each transmission and guidance unit comprises a male element (9) mounted on one of the scroll plates and a facing female element (10) mounted on the facing scroll plate. Each transmission and guidance unit (9,10) comprises an internal ring (11) mounted for angular displacement in the opening of the female element (10), the internal ring having therein a slot (18) wherein the male element (9) of the transmission and guidance unit slides. The male elements (9) of the three transmission and guidance units (9,10) are supported and guided by respective support elements (13) on a common external guide ring (11). A liquid injection system comprises a liquid channel (20) which is connected with bleed holes (21).