A uniqueness theorem for a static electric or magnetic field in an isotropic but saturable medium is presented. We show that if, in a given region,BandHare appropriately related and Maxwell's equations are satisfied, and if over the boundary of that region either normalBor tangentialHis prescribed, then bothBandHare unique in that region. A similar statement can be made aboutDandEin an electric field calculation if, in addition, we assume that the region is free of electric charge.