Methods based on Monte Carlo solutions of the transport equation for the joint probability density function (pdf) of scalars are considered to be among the most promising approaches for modeling turbulent reactive flows. For the treatment of convection and diffusion two approaches are well established, either from Eulerian or Lagrangian point of view. Simply speaking, the former is computationally less expensive but also less accurate than the latter one. In this paper we provide an extension of a previous analysis of numerical diffusion of Eulerian schemes to two-dimensional flows in order to shed light on the shortcomings of this approach. For convergence acceleration, local rime stepping is extended to Lagrangian pdf methods. Furthermore, the adaption of the Continuous Mixing Model to unequal particle weights is presented. The differences between the Eulerian and Lagrangian approaches are analyzed by application to simple test problems and by simulation of a supersonic hydrogen-air diffusion flame using a chemical scheme consisting of seven elementary reactions. (C) 2001 by The Combustion Institute.