The steady, compressible, turbulent boundary-layer flow, with heat and mass transfer, over a wedge, is numerically studied. The fluid is considered to be a Newtonian ideal gas (air) and it is subject to a constant velocity of suction/injection applied globally or locally to the wedge. The Reynolds-Averaged Boundary-Layer (RABL) equations and their boundary conditions are transformed using the compressible Falkner-Skan transformation. The resulting coupled and nonlinear system of PIDEs is solved using the Keller-box method. For the eddy-kinematic viscosity the Cebeci-Smith and Baldwin-Lomax turbulent models are employed. For the turbulent Prandtl number the extended model of Kays-Crawford is used. Numerical calculations are carried out for the case of an adiabatic, cooled or heated wall and for different values of the parameters of the problem under consideration. The obtained results show that the flow field can be controlled by the suction/injection velocity and it is influenced by the dimensionless pressure parameter m. (C) 2008 Elsevier Ltd. All rights reserved.