Small-angle x-ray scattering (SAXS) experiments using synchrotron radiation were carried out for supercritical water along isotherms at the temperatures T=660.0, 661.5, 663.0, 677.0, and 687.5 K, from a gaslike density region to a liquidlike one, including an intermediate density region. The high-temperature and high-pressure sample holder for SAXS measurements suitable for supercritical water was redesigned for more precise measurements. The curves illustrating the density dependence of density fluctuations and correlation lengths show a slight shift of the maximum from critical isochore. The deviations become larger with increasing temperature. The results for the density fluctuations and correlation lengths for supercritical water are compared with those for supercritical CO2 and CF3H at T/T-c=1.02 and 1.06. The comparison allows us to draw the conclusion that the behavior in the long-range inhomogeneity of water in the supercritical state is in discord with the ordinary behaviors for other molecular substances. Density fluctuations in water are also compared with those of Ar and Hg calculated thermodynamically by use of the equations of state. The correlation of the symmetry between the contour of density fluctuations and the vapor-liquid coexistence curve is discussed. (C) 2000 American Institute of Physics. [S0021-9606(00)50108-1].