A hydrodynamic clutch device has at least one pump wheel, connected to a drive by way of a clutch housing, and a turbine wheel, connected to a takeoff, to form a hydrodynamic circuit. The device also has a bridging clutch with at least one piston, which can shift between a released position and an engaged position, and at least one friction surface acting between this piston and an adjacent support to connect the drive to the takeoff. When the piston is in the released position, the bridging clutch allows the hydrodynamic circuit to be used to transmit at least most of the torque between the drive and takeoff, whereas, when the piston is in the engaged position, the bridging clutch produces a bypass around the hydrodynamic circuit for the transmission of torque. A pressure circuit is provided in the form of a two-line system with a first pressure medium line to supply the hydrodynamic circuit with clutch fluid and with a second pressure medium line to supply a pressure space assigned to the piston with clutch fluid. A flow velocity influencing device is assigned to the hydrodynamic circuit and/or to the pressure space, located in each case axially between the piston and a component at least indirectly adjacent to the piston.