A model has been developed for the behavior of an isolated fluid drop of a single compound immersed into another compound in finite, quiescent surroundings at supercritical conditions. The model is based upon fluctuation theory which accounts for both Soret and Dufour effects in the calculation of the transport matrix relating molar and heat fluxes to the transport properties and the thermodynamic variables. The transport properties have been modeled over a wide range of pressure and temperature variation applicable to LOx-H-2 conditions in rocket chambers, and the form of the chemical potentials is valid for a general fluid. The equations of state have been calculated using a previously-derived, computationally-efficient and accurate protocol. Results obtained for the LOx-H-2 system show that the supercritical behavior is essentially one of diffusion. The temperature profile relaxes fastest followed by the density and lastly by the mass fraction profile. An effective Lewis number calculated using theory derived elsewhere shows that it is larger by approximately a factor of 40 than the traditional Lewis number. The parametric variations show that gradients increasingly persist with increasing fluid drop size or pressure, and with decreasing temperature. The implication of these results upon accurate measurements of fluid drop size under supercritical conditions is discussed.