This study deals with a spin system constituted of three nonequivalent protons, two of them originating from para-hydrogen (p-H(2)) after a hydrogenation reaction carried out in the earth magnetic field. It is shown that three singlet states are created provided indirect (J) couplings exist between the three spins, implying hyperpolarization transfer toward the third spin. Upon insertion of the sample in the NMR (Nuclear Magnetic Resonance) high field magnet, the following events occur: (i) the longitudinal two-spin orders which are parts of the singlet states survive; (ii) the other two terms (of these singlet states) tend to be destroyed by magnetic field gradients but at the same time are partly converted into differences of longitudinal polarizations. Nuclear spin relaxation is studied by appropriate NMR measurements when evolution takes place in the high field magnet or in the earth field. In the former case, relaxation is classical although complicated by numerous relaxation rates associated with both longitudinal two-spin orders and longitudinal polarizations. In the latter case, an equilibration between the singlet states first occur, their disappearance being thereafter driven by relaxation rates which remain very small because of the absence of any dipolar contribution. Thus, even in the case of a three-spin system, long-lived states exist; this unexpected property could be very useful for many applications.