  We develop a theory of spin relaxation in Zeeman-splitted superconducting
films at low temperatures. A new mechanism of spin relaxation, specific only
for Zeeman-splitted superconductors is proposed. It can explain the extremely
high spin relaxation lengths, experimentally observed in Zeeman-splitted
superconductors, and their strong growth with the magnetic field. In the
framework of this mechanism the observed spin signal is formed by the
spin-independent nonequilibrium quasiparticle distribution weighted by the
spin-split DOS. We demonstrate that the relaxation length of such a spin signal
is determined by the energy relaxation length at energies of the order of the
superconducting gap.
