The thermal conductivity of four binary aqueous NaBr solutions of (10, 20, 30, and 38) mass %, three binary aqueous KBr solutions of (10, 20, and 30) mass %, and three ternary aqueous NaBr + KBr solutions of (10NaBr + 5KBr, 10NaBr + 10KBr, and 10NaBr + 20KBr) mass % have been measured with a concentric-cylinder (steady-state) technique. Measurements were made near the saturation curve of (0.1 to 2) MPa and at two isobars of (10 and 40) MPa. The range of temperature was (294 to 577) K. The total uncertainty in the thermal conductivity, pressure, temperature, and composition measurements was estimated to be less than 2%, 0.05%, 30 mK, and 0.02%, respectively. The temperature, pressure, and concentration dependence of the thermal conductivity of binary and ternary solutions were studied. The measured values of thermal conductivity were compared with data and correlations reported in the literature. The reliability and accuracy of the experimental method was confirmed with measurements on pure water with well-known thermal conductivity values. The experimental and calculated values of thermal conductivity for pure water from the IAPWS formulation show excellent agreement within their experimental uncertainties (AAD within 0.51%) in the temperature range from (290 to 575) K and at pressures up to 40 MPa. Correlation equations for the thermal conductivity of the binary solutions studied were obtained as a function of temperature, pressure, and composition by a least-squares method from the experimental data. The AAD between measured and calculated values from this correlation for the thermal conductivity was 1.5%.