The EXFIDIS project has for ambition to investigate a physics still not described this day, that of non equilibrium electrical discharges created by extremely transient and intense fields in standard conditions of pressure and temperature. For that purpose, research groups of LAPLACE ( Toulouse), LPGP ( Orsay), GREMI ( Orléans) and CORIA (Rouen), supported by a group of the LNHB (SACLAY CEA) as external service provider, suggest sharing their know-how and their knowledge in the field of non equilibrium pulsed discharges and X rays. The experimental studies and of modelling which they propose focus on configurations of asymmetric electrodes often used for applications (point-to-plane, multi-points/plane, wire/plane), without any auxiliary pre-ionization system, in air and atmospheric gases mixtures of nitrogen, oxygen and water vapor, to which will come to be added, in low concentration, acetone, representative of a polluting molecule, or some propane, representative of a flammable gas. The objectives of the project are at first to take into account the specific effects induced by the very strong values of the electric field, at the same time in a two-dimensional model of the discharge and in studies of very accurate experimental characterization. The application of extreme overvoltages (> 400 %) over less than a few nanoseconds has to bring us to reconsider the classical physics of the streamer used to describe discharges at atmospheric pressure, by analyzing the new mechanisms which could be associated there (diffuse regime, generation of " runaway " electrons and X radiation, invalidity of the local field equilibrium hypothesis). The recent marketing of reliable, compact and adjustable generators, allowing to reach extremely brief fronts of rise of the order of nanosecond and voltage pulses of hundred of kilovolts on about ten nanoseconds, opens very interesting possibilities for the experimental study of these discharges. The fundamental objectives of the project EXFIDIS impose us to use an elementary point-to-plane configuration of electrodes, to allow to obtain measures of different physical quantities (densities of electrons, atoms, molecules, radiative or metastable excited species, temperatures, electric field, UV photons and X) resolved in time (from nanoseconds to tens of microseconds), and in space (some centimetres). The modelling of this discharge is facilitated by the use of a numerical code with a not-structured mesh, integrating at first an equation of energy for electrons and, secondly, a “Particle In Cell” (PIC) method to follow electrons and photons of high energy (< 50 keV). The modelling of the post-discharge is also considered, relying on kinetics studies in pre-ionized discharges. The ability of the “EXtreme FIeld DIScharge” to be used for environmental applications such as gas treatment or synthesis, or energy field applications such as ignition or flow control, which are all very topical subjects, will be investigated and demonstrated. By realizing and by studying a multi-points/plane reactor, the EXFIDIS project will then try to open the way to the development of innovative and more efficient “plasma” reactors for air cleanup. An outcome of the project will be to propose solutions of implementation of reactors of large volume using discharges with controlled intense transient fields.