In the binary radio pulsar system J0737-3039 the faster pulsar A is eclipsed once per orbit while the slower pulsar B shows orbital-dependent variations of intensity. This gives us an exceptional opportunity to study inner magnetospheres of neutron stars and their winds. We construct a model of eclipses which reproduces the observed light curve up to intricate details and proves the long standing assumption of dipolar magnetic fields of neutron stars. In addition, interaction of pulsar B magnetosphere with pulsar A wind produces orbital variations of observed B intensity.