A correlation of the properties of compressed fluids is presented in terms of a seven-coefficient reduced equation which is common to a group of fluids called corresponding fluids, thirteen of which are investigated here. With three characteristic constants for each fluid, this one equation provides an accurate equation of state and allows the calculation of the thermodynamic properties derivable therefrom. The equation is valid in the compressed fluid region for densities ranging roughly between two and three times the critical density, as determined for each fluid by the range in which its unit compressibility line (UCL) is linear within a few parts per ten thousand. The form of the equation is determined by the fact that isotherms of the residual Helmholtz energy, A(r), have a minimum on the UCL. The coefficients are evaluated by a simultaneous least-squares fitting of the P rho T behavior of the published modified Benedict-Webb-Rubin (MBWR) or Schmidt-Wagner (SW) equations of state for five fluids : oxygen, argon, ethane, ethylene, and propane. The reduced equation is used to calculate the density, rho, as a function of T and P, agreeing within experimental error with the MBWR or SW equations for these five fluids. It is applied with similar success to n-butane, isobutane, nitrogen trifluoride, methane, and carbon monoxide. The equation also succeeds in representing accurately rho(T,P) for sets of original experimental data for nitrogen, krypton, and xenon. Thermodynamic properties that can be calculated from the reduced equation include the difference between the heat capacities, C-P - C-V, at any point in the region and isothermal changes in the thermodynamic properties E, H, S, A, G, Cp, and Cv between any two densities in this range. A table is given showing the favorable comparison between these changes as calculated from the reduced equation and from the SW equations for ethane.