A boundary-layer integral method analysis is set up for compressible laminar flow in a S3^mmetric corner with var}dng angle and streamwise pressure gradient. I t represents an extension and modification of the constant density analysis of Loitsianskii and Bolshakov. The analysis is applied to the case of constant pressure, constant corner angle, and isothermal surfaces, for which the Crocco velocity-enthalpy relation holds. Although simplifying assumptions limit the quantitative accuracy outside the 60° to 120° angle range, some qualitative trends are probably correct outside this range. The limiting cases near 0° and 180° are not considered. Favorable agreement between some results obtained by the integral method and by other methods is demonstrated for the isothermal, constant-density case. Results show an increasingly sharp merger of the outermost isovels of streamwise velocity as the Mach number increases. This sharp merging of the outer isovels is increased by increasing corner angle and by insulation or heating of the surfaces. Within the interior of the viscous layer the spreading or contraction of the disturbed region of merging is influenced by surface heattransfer conditions. Surface shear and heat flux are decreased in the disturbed region, and are zero at the apex. For cases corresponding roughly to the higher Mach numbers or wider corner angles, the "specific momentum-area" exhibits the same decrease with Mach number as its two-dimensional counterpart, whereas the "specific displacement-area," a measure of streamtube dilation, increases more rapidly with Mach number than the comparable two-dimensional parameter. u V v W w 7 A*