It has recently been shown that in spin-pair systems a new type of spin ordering occurs under magnetic fields. In the present paper, the spin ordering in general cases of the inter-pair exchange interaction and the thermodynamical properties of these systems are investigated on the basis of molecular field theory. Various types of spin ordering appear depending on the strength of the inter-pair exchange interaction and the external magnetic field. The specific heat originating from the short range order of spins in a one-dimensional lattice is also calculated for a purpose of comparison with experiments in Cu(NO_3)_22.5H_2O
