Approaches based on probability density functions (PDF) are a natural choice for the simulation of high-speed and supersonic turbulent reacting flows due to their ability to represent chemical sources in closed form. This paper aims in particular at the application of scalar and joint scalar-velocity-turbulent frequency PDF methods to supersonic combustion. Because transport equation PDF simulations of supersonic combustion are still rare, emphasis is placed on the peculiarities of this kind of flow. The paper reports detailed results for two supersonic hydrogen-air non-premixed flames and makes comparison with available experimental data. A reaction scheme consisting of seven elementary reactions is considered, which provides an adequate description of chemical kinetics. As mixing models still are the weakest point of transport equation PDF methods, the three most frequently applied formulations have been investigated. Only minor differences are observed for the supersonic test cases. Moreover, these simulations represent the first published application of joint scalar-velocity-turbulent frequency PDF calculations to supersonic flows with complex geometry and hydrogen chemistry. It is shown that significant improvements are achieved by the joint PDF approach for one of two high speed reacting flows investigated. Results are somewhat unconclusive in the other case, partly due to uncertainties in the experimental setup. (C) 2003 The Combustion Institute. All rights reserved.