Population Balance Equations (PBE) describe complex processes where the accurate prediction of the dispersed phase plays a major role for the overall behavior of the system. However, the solution of this type of equation is computationally intensive. In this paper, a least squares spectral method for solving the population balance in d = 1, 2, 3 physical domains, p = 1.... property domain and time is discussed. In the presented approach, the solution is found as the function that minimizes the residual function in the least squares sense. The capability of the method is shown by using some model problems related to the advective transport of the density function which describes the dispersed phase. (c) 2006 Elsevier Ltd. All rights reserved.