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The main purpose of my thesis is to examine some electrodynamic properties of binary pulsars, trying to understand the peculiar physical processes that can happen in their magnetospheres; the ultimate aim is to discuss if such systems can be the source of the observed flux of cosmic rays between the knee and the ankle, since the mechanisms of acceleration for the cosmic rays in this range of energies are still unknown. Attention around binary pulsars has arisen after the recent discovery (December 2003) of the first double neutron star system in which both the stars are visible as pulsars (PSR J0737-3039); the inspection of the physical features of this binary pulsar has led to some intriguing possibilities up to now unexplored. In this thesis I will first of all review what is already known about the main properties of this binary system. I will describe in particular the possibility to go further in the verification of the predictions of general relativity with the so-called post-Keplerian parameters; I will discuss the possibility of studying the optical properties of the magnetospheres, since the inclination angle of the orbit is nearly 90