Electro Discharge Machining (EDM) is an attractive subtractive method for complex 3d structurization of hard and very hard conductive and semi-conductive materials. The machining capabilities of a material do not depend on its hardness but on its electric conductibility and its melting point. The absence of any mechanical interaction between tool (the electrode) and machined part makes the electroerosion a well-adapted process for micro-structurization. In the passage from the macro to the micro-electroerosion (µEDM), some of the elements of the machine have to be adapted in order to improve the performances and to obtain accurate movements. The goal is to manufacture millimeters-sized shapes with an accuracy of a hundred of nanometers. This thesis deals the problem of the µEDM with a three degrees of freedom (DOF) mechanism, based on a parallel kinematics and flexure joints (the Delta3 robot). In addition to its high accuracy (5 nm) and high bandwidth (500 Hz), the Delta3 robot has the particularity of being free of backlash, wear and stick-slip phenomena. These performances have allowed to verify the importance of the time constants in the servo loop of the process, by many experiences of micro-drilling. Simulations have demonstrated the advantages brought by the dynamic, in the improvement of the µEDM process. Bad flushing conditions and very small gaps (<10 µm), generate elevated gradients of contamination, to which the frequency response of the machine must be adapted. Simulations have shown that the balance between the material removal rate and the evacuation rate can be improved by adjusting the electrode-part distance at a frequency of a few hundreds of hertz. These back and forth movements have to be fast and accurate: first, to adjust quickly and precisely the breaking voltage distance and second, to guarantee a good machining accuracy. An industrial version of the prototype finalized during this thesis will be commercialized soon by AGIE (the company that supported this work).