In this work it has been found that the conventional spin relaxation equations are not valid for the hyperpolarized spins. New longitudinal relaxation equations for the dipole- dipole coupled hyperpolarized spins have been derived. These new equations predict that the longitudinal magnetization relaxation for hyperpolarized spins is, in general, bi- exponential instead single exponential. They also predict that for dipole-dipole coupled hyperpolarized spins the steady state longitudinal magnetization is larger than the thermal equilibrium magnetization. These findings are useful as the base-line information for accurate analysis of the effects of the paramagnetic sources on relaxation of hyperpolarized spins in living body.