The steady state of a two spin system coupled to an isotropic environment and to each other through a dipolar interaction and under irradiation by a monochromatic, circularly polarized radio frequency field is determined ab initio using thermodynamic arguments. This steady state is used to describe the well known nuclear Overhauser effect in liquids. The steady state is also derived from the Solomon-Bloch set of equations used to describe the driven spin. It is shown that in the limit of weak driving, the two solutions coincide. (C) 1999 American Institute of Physics. [S0021-9606(99)71210-9].