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Gold has suggested that pulsars are rotating magnetic neutron stars which formed in supernova explo- sions. We have investigated the simplest such model, one in which the magnetic dipole moment is aligned with the rotation axis. Our conclusions are as follows: In spite of its intense surface gravity, the star must possess a dense magnetosphere. The particles in the region threaded by those field lines which close within the light cylinder (of radius 5 X 1O~ p cm, where P sec is the stellar rotation period) rotate with the star. In the corotating zone the space-charge den- sity is 7 X 102 BZ/P electronic charges per cm3, where B~ (in gauss) is the component of magnetic field parallel to the rotation axis. The field lines which extend beyond the light cylinder close in a boundary zone near the supernova shell. Charged particles escape along these lines and are electrostatically accelerated up to energies of 3 X 1O'~ ZR63 B12 p-2 eV in the boundary zone. (Here, the stellar radius is R6 X 106 cm, and the magnetic field at the polar surface is B12 X 1012 gauss) Beyond the light cylinder the magnetic field becomes pre- dominantly toroidal. Its strength is 6 X 1O~ R63 B12 P~ ~ gauss at a distance of r~0 parsecs from the central star. The magnetic torque on the star causes its rotation period to lengthen at the rate P~ dP/dt = 10-8 B122 R64 p-2 M-' yr1 for an 211 solar-mass star. The rotational energy lost by the star is trans- ported out by the electromagnetic field and is then transmitted to the particles in the boundary zone. We compare our model with the observed properties of the Crab pulsar (NP 0332) and CP 1919