The appliance (1) for the transfer of biomedical fluids between hospital receptacles (R, P), comprises: a syringe device (2) comprising a hollow syringe body (3) for containing the biomedical fluid and one sliding piston (4) fitted sealed in the syringe body (3), the latter haying a first end (5), which has joining means for joining with a hospital receptacle (R, P), and a second open end (6) - a grippable operating device (12), comprising a fastening seat (13) which can be coupled in a removable way to the second end (6) of the syringe device (2), which comprises a thrust rod (15) suitable for sliding through the second end (6) temporary fastening means for coupling the rod (15) and the piston (4) in a releasable way motor means ( 17) for operating the thrust rod (15) control means (18) connected to the motor means (17) so as to control both the volumetric dosage of the quantity of fluid taken from a first hospital receptacle (R) or dispensed in a second hospital receptacle (P). Storage means (21) are mounted on the syringe device (2), and the operating device (12) comprises reading/writing means (22) for reading and writing information from/on the storage means (21), the control means comprising a processing unit (18) able to control the reading/writing means (22).