A pump is formed by a housing (10) having an inlet (11) for connection to a source of fluid and an outlet (12) for pumped fluid. A rotor (15) is rotatable within the housing and the inlet (11) and the outlet (12) are spaced apart around the path of the rotor (15) in the housing. The rotor (15) has surfaces (16a, 16b, 16c, 16d) that form, with the housing (10), closed chambers (18a, 18b, 18c, 18d) which travel around the housing (10) to convey fluid from the inlet (11) to the outlet (12). The housing (10) carries a seal (14) that is located between the inlet (11) and the outlet (12) in the direction of travel of the rotor (15). The seal (14) co-operates with the rotor surfaces (16a, 16b, 16c, 16d) as the surfaces (16a, 16b, 16c, 16d) pass between the outlet (12) and the inlet (11) to prevent the formation of a chamber during said passage and so prevent fluid flow from the outlet (12) to the inlet (11). Such a pump is easily and cheaply produced and is particularly useful in medical applications.