This paper describes the application of the Eulerian, single-point, single-time joint-scalar probability density function (pdf) equation for predicting the evolution of turbulent jet diffusion flames. The basic geometry under investigation was a round jet of gaseous hydrocarbon (CH4 or C3H8) issuing into unconfined, stagnant air for which detailed measurements were available. The main emphasis of the work was the prediction of the combustion characteristics including the concentrations of CO, CO2, H-2, H2O, O-2 and UHC and temperature. A finite-volume procedure was applied to obtain the velocity field with the k-epsilon or alternatively a second moment Reynolds stress closure being used to describe turbulent transport. The scalar field was represented through the modelled evolution equation for the scalar pdf and solved using a Monte Carlo simulation. The pdf equation employed gradient transport modelling to represent the turbulent diffusion, and the molecular mixing term was modelled by the LMSE and coalescence-dispersion closures. The ＇source＇ terms for chemical reaction were represented via global and systematically reduced schemes. The thermochemistry was tabulated on an ＇once and for all＇ basis and the results stored in a look-up table; multi-linear interpolation was employed in order to extract the necessary information from the tables. The results demonstrate that the global reaction scheme leads to satisfactory predictions for the mixing field, fuel consumption and major products of reaction (e.g., CO2). However the levels of CO were consistently over predicted, regardless of the turbulence or mixing models employed; in fact the results showed little sensitivity to the models. In contrast with the systematically reduced reaction mechanism the effect of the mixing model appeared to be significant; it was difficult to generate a stable flame and with the LMSE extinction was predicted. The inability of the systematically reduced chemical scheme to maintain stable combustion (despite the fact that the measurements and the predictions using the global scheme suggest otherwise) raises doubts to its viability in the current pdf modelling approach.