The evolution of magnetic fields that are initially confined relativel
y close to the surface of neutron stars is discussed. The influence of
the cooling of the star on the conductivity and on the rate of the ma
gnetic field dissipation is taken into account. The influence of the f
ield decay on the variation of the spin rate is analyzed under assumpt
ion of spin slow-down due to the energy losses via magnetic dipole rad
iation. The evolutionary tracks of single neutron stars in a diagram o
f surface magnetic field versus spin period are computed.