The problem of simultaneous convection and radiation in the laminar boundary layer on a flat plate is formulated and solved. The plate surface is assumed black and the fluid medium is a perfect gas for which the mass absorption coefficient for radiation is considered to be independent of frequency and temperature. The solution is of the iterative type and includes effects of viscous dissipation, secondary emission and absorption, and incident external radiative fluxes. Illustrative examples of temperature profiles and local and average heat transfer rates are presented.