Since it was first proposed, the direct quadrature method of moments (DQMOM) has been employed for the solution of population balance equations in a wide range of applications. One of its most interesting features is that it can be easily employed for the solution of multivariate population balances, which are often necessary to obtain complete information on the particle population under study. In addition, DQMOM can be easily implemented in computational fluid dynamic (CFD) codes, and requires low computational costs. A bivariate formulation of the population balance equation that is particularly suited for modeling nanoparticles formation in flames is presented. The use of DQMOM for the solution of bivariate population balances is explored in detail, and the method is validated by comparison with simulations carried out with a code based on Monte Carlo methods (MCM). Particular attention is devoted to the choice of the moments to be tracked in DQMOM, in order to obtain a stable algorithm and reliable and accurate results. Eventually the method is implemented in a commercial CFD code, and a real application is studied: soot nanoparticles formation in turbulent combustion processes. (c) 2007 American Institute of Chemical Engineers.