A vane machine comprises an inner rotor (28) and an outer rotor (51). A plurality of radially extending vane elements (32) separates first vane chambers (89) from one another. The van elements (32), with a radially inner end region (34), are accommodated in the inner rotor (28) in a radially displaceable manner and, with a radially outer end region (36), are accommodated in the outer rotor (51) in a pivotable manner. It is proposed that the radially inner end regions (34) of the vane elements (32) be accommodated in the inner rotor (28) at a fixed angle and that the outer rotor (51) comprise individual shoes (38) which are separate for each vane element (32) and in which the vane elements (32) are accommodated in a pivotable manner.