On a fixture for electro-chemical machining for the production of long, curved cavities (11) in a component (12), the working electrode (3) of the electro-chemical machining tool (1) is connected to a guide body (1a) which moveably rests against the inner walls of the respective cavity by means of power-actuated guide elements (2), with the guide body being connected to a flexurally soft and torsionally stiff guide linkage (5) coupled to a feed and rotary drive. Control of the movement of the guide body is accomplished in dependence of at least one wall thickness measured with a measuring device (13, 14) during feed movement.