Most De Dietrich oven hinges work on a similar principle (although I don't know the FB2727):
They have a retaining clip as part of the hinge unit and when the door is opened fully this can be swung into place: It keeps the hinge spring tensioned.
Do this to both hinges then close the door and the hinge mechanisms will pull free from the main unit and the door will come away.
The hinge mechanism itself can be removed by sliding out the front glass of the door then removing the retaining screws usually accessed from inside.
Once the new hinge is fitted it requires tensioning (to be in the same state as the other hinge) once this has been done the door can be relocated into its original (closed) position. Open the door carefully making sure the appropriate sections of the hinge remain located inside the main unit; until the door is fully open. The retaining clips can now be swung away and closing the door will complete the work.
JemP, September 2009