The Eurofighter has a transponder that can be switched off, similar to a Cessna. By switching off the transponder, the aircraft becomes invisible to cooperative surveillance. This means the aircraft will not be detected by secondary radar and active multilateration. However, the aircraft can still be detected by primary radar because that does not rely on the transponder.
Civil ATC centres sometimes use only secondary radar, so in such a case the aircraft can become invisible when the transponder is switched off.
Military air traffic control and air defence systems do not rely so much on cooperative surveillance, mainly because you can't expect the enemy to cooperate. Therefore hiding a Eurofighter from military ATC by switching off the transponder is doomed to fail.
