The invention relates to a tank device (1) for storing a gaseous medium, in particular hydrogen, comprising a valve device (100) and a tank container (200), wherein the valve device (100) comprises a valve housing (102), in which valve housing (102) a pilot valve element (24) that can be moved along a longitudinal axis (101) of the tank container (100) is disposed. The pilot valve element (24) cooperates with a first sealing seat (18) to open and close a passage opening (20) and thus forms a pilot valve (240), wherein the valve device (2) comprises a solenoid coil (32) by means of which solenoid coil (32) the pilot valve element (24) can be moved along the longitudinal axis (101) of the tank device (1). A main valve element (12) is furthermore disposed in the valve housing (102), which main valve element (12) cooperates with a second sealing seat (6) to open and close a passage opening (8) and thus forms a main valve (120), wherein the second sealing seat (6) is configured as a conical shoulder (36) on the valve housing (102). In addition, a permanent magnet (17) is disposed at one end (42) of the pilot valve element (24), which permanent magnet (17) is disposed in the valve device (100) such that a positive pole element (170) of the permanent magnet (17) is disposed in the direction of a housing cover (28) of the valve device (100) and a negative pole element (171) of the permanent magnet (17) is disposed in the direction of the tank container (200), wherein the permanent magnet (17) is disposed in a positive pole region (51) of a permanent magnetic field (52) generated by the solenoid coil (32) when the solenoid coil (32) is energized.