The invention relates to a catheter device (100) comprising a catheter (68) for insertion into a living being and at least one lumen (69, 70, 74, 79) for guiding a fluid flow within a section of the catheter device, and comprising a valve for controlling a fluid flow, in particular through a catheter, having a valve control chamber (12, 12a), into which an inlet opening (1a) of an inlet channel (1) and an outlet opening (2a) of an outlet channel (2) open, and further having a closure element (5, 13, 17) which can be moved in the valve control chamber (12, 12a) in a controlled manner and which, in at least a first position (I), closes the outlet opening (2a), in at least a second position (II) closes the inlet opening (1a), and which, in at least a third position (III), keeps open a connecting channel between the inlet opening (1a) and the outlet opening (2a), a valve train (A, A′, B, B′, 3, 14, 18) being provided and optionally moving the closure element (5, 13, 17) to at least the first, second or third position, and the at least one lumen (68, 70, 74, 79) being fluidically connected to the inlet channel or the outlet channel.