Densities of sodium hydroxide solutions at concentrations of 0.1 less than or similar to m/mol center dot kg(-1) less than or similar to 8 have been measured by vibrating-tube densimetry over the temperature range 323 <= T/K <= 573 at a pressure of 10 MPa. The purpose-built densimeter, which is capable of measuring densities of corrosive fluids at temperatures up to 573 K and pressures up to 30 MPa, has a platinum-rhodium vibrating tube with inlet/outlet tubes of platinum and an optical detection system. Calibrations were carried out with water and aqueous solutions of sodium chloride at temperatures up to 523 K. At higher temperatures, nitrogen was substituted as the auxiliary density reference because of uncertainties in the NaCl(aq) densities. The apparent molar volumes of NaOH(aq) calculated from the measured densities were fitted with an extended Redlich-Meyer equation. The present results are in good agreement with literature data but are more precise. The current global accuracy in the densities of NaOH(aq) appears to be about 0.1 %, being significantly better at lower concentrations and temperatures but slightly worse at higher concentrations and temperatures. More accurate knowledge of the densities of the reference materials (other than water) used for calibrating vibrating-tube densimeters under extreme conditions is probably required to improve the accuracy of such data.