  In this thesis we address the question of {\em the evolution of the magnetic
field in neutron stars}. There has been sufficient observational indication
suggesting a causal connection between the binary history of neutron stars and
the evolution of their magnetic field. In particular, it is believed that the
generation of the low-field millisecond pulsars is a consequence of the
processing of normal high-field neutron stars in binary systems. Therefore, in
this thesis we try to understand the mechanism of field evolution in neutron
stars that are members of binary systems with an aim to understand the problem
of millisecond pulsar generation. To this end we have looked at four related
problems as described below : 1. the effect of diamagnetic screening on the
final field of a neutron star accreting material from its binary companion; 2.
evolution of magnetic flux located in the crust of an accreting neutron star;
3. application of the above-mentioned model to real systems and a comparison
with observations; 4. an investigation into the consequences of magnetic flux
being initially located in the core of the star and its observational
implications.

Solar and Stellar Astrophysics;High Energy Astrophysical Phenomena