Device for adapting the actual tyre pressure of at least one tyre (8; 8') of a wheel of an axle of a vehicle to a current set tyre pressure during travel, comprising: a) a chassis-side central apparatus which either feeds the current set tyre pressure into a connection (20; 20'), which rotates with the wheel, of a wheel-related pneumatic pressure control apparatus (6; 6') in order to adapt the actual tyre pressure to the set tyre pressure, or vents this connection (20; 20') if the actual tyre pressure is equal to the set tyre pressure, wherein b) the pressure control apparatus (6, 6') contains at least one further connection (23; 23') to which the actual tyre pressure can be applied, and c) at least one control valve (11; 11') having an open position which connects the one connection to the further connection (23; 23') and having a closed position which closes this connection, wherein the control valve (11; 11') is controlled pneumatically in opposite directions, and one of its pneumatic control connections (16a; 16a') is connected to the one connection (20; 20'), wherein d) the pressure control apparatus (6; 6') contains at least one pilot valve (13; 24') which performs pilot control of the control valve (11; 11') and which feeds either the pressure present at the one connection (20; 20') or the actual tyre pressure present at the further connection (23; 23') into the other pneumatic control connection (16b; 16b') of the control valve (11; 11') or prevents such feeding in, wherein e) the pilot valve (13; 24') is controlled pneumatically at least by a pressure present at the one connection (20; 20') and/or at least by the actual tyre pressure present at the further connection (23; 23'), characterised in that f) the pressure control apparatus (6; 6') has a bypass line (10; 10') which bypasses the control valve (11; 11') and the pilot valve (13; 24') and connects the one connection to the further connection (23; 23') and has a non-return valve (14; 14') which opens in the inflation direction of the tyre (8; 8') and closes in the venting direction of the tyre (8; 8'). a) a chassis-side central apparatus which either feeds the current set tyre pressure into a connection (20; 20'), which rotates with the wheel, of a wheel-related pneumatic pressure control apparatus (6; 6') in order to adapt the actual tyre pressure to the set tyre pressure, or vents this connection (20; 20') if the actual tyre pressure is equal to the set tyre pressure, wherein b) the pressure control apparatus (6, 6') contains at least one further connection (23; 23') to which the actual tyre pressure can be applied, and c) at least one control valve (11; 11') having an open position which connects the one connection to the further connection (23; 23') and having a closed position which closes this connection, wherein the control valve (11; 11') is controlled pneumatically in opposite directions, and one of its pneumatic control connections (16a; 16a') is connected to the one connection (20; 20'), wherein d) the pressure control apparatus (6; 6') contains at least one pilot valve (13; 24') which performs pilot control of the control valve (11; 11') and which feeds either the pressure present at the one connection (20; 20') or the actual tyre pressure present at the further connection (23; 23') into the other pneumatic control connection (16b; 16b') of the control valve (11; 11') or prevents such feeding in, wherein e) the pilot valve (13; 24') is controlled pneumatically at least by a pressure present at the one connection (20; 20') and/or at least by the actual tyre pressure present at the further connection (23; 23'), characterised in that f) the pressure control apparatus (6; 6') has a bypass line (10; 10') which bypasses the control valve (11; 11') and the pilot valve (13; 24') and connects the one connection to the further connection (23; 23') and has a non-return valve (14; 14') which opens in the inflation direction of the tyre (8; 8') and closes in the venting direction of the tyre (8; 8').