Abstract: Control structure for extending and retracting at least two stabilizing arms (2) in a drill or core device, in particular stabilizing arms (2) in a drill or core bit (3), each arm (2) having an extremity pivoted around an axis (6) parallel to the axis (4) of the drill bit, comprising, per arm (2), a piston (8) provided for pivoting the arm (2) around said axis (6) so that it takes the arm to two extreme positions, a first position wherein it is housed in the bit (3) and a second position wherein it projects with respect to this bit. The control structure (10) and synchronization means (11) are provided respectively for displacing the pistons (8) under the influence of the drill fluid and for making the pistons (8) act substantially simultaneously in the same direction and to the same amplitude.