Vapor pressures for n-hexane-c-hexane were measured at extremely low concentrations of n-hexane. The vapor pressure data seemed to indicate within the experimental uncertainty that, in the range of the mole fraction of n-hexane x(nH) < 0.015, the solution obeys Henry's law. However, the excess partial molar enthalpy of n-hexane and c-hexane measured by a sensitive microcalorimeter showed that the Henry's law is not operative above x(nH) or x(cH) approximate to 2 x 10(-4), the lowest accessible for the calorimetry technique available at present. The excess partial molar enthalpies of the following solutes were also determined in aqueous solutions in an extremely dilute region. Within the experimental technique at our disposal, we could not locate a finite range of Henry's law. Thus, whether the solute-solute interaction becomes actually absent or whether such absence depends on the nature of the solvent (H2O or organic) cannot be addressed at present. For aqueous solutions, however, the lower limits of the mole fraction of a solute, above which the solutions behave as non-Henry-like, were found by an order of magnitude lower : 1 x 10(-5) for 2-butoxyethanol; 3 x 10(-5) for tert-butyl alcohol; 2 x 10(-5) for glycerol; 3 x 10(-5) for urea.