To conduct a fluid, the transducer has a flow tube which in operation is vibrated by an excitation assembly and whose inlet-side and outlet-side vibrations are sensed by means of a sensor arrangement. To produce shear forces in the fluid, the flow tube is at least intermittently excited into torsional vibrations about a longitudinal flow-tube axis. The transducer further comprises a torsional vibration absorber which is fixed to the flow tube and which in operation covibrates with the torsionally vibrating flow tube, thus producing reactive torques which at least partially balance torques developed in the vibrating flow tube. One of the advantages of the transducer disclosed is that it is dynamically balanced to a large extent even in the face of variations in fluid density or viscosity.