One way to model and simulate the dispersed phase in a two-phase flow is to track the discrete elements through a fluctuating fluid field by solving their equations of motion. This approach is called Lagrangian. In this frame, it has been shown previously that widely used discretization methods for integrating the particle equation of motion in bubbly flows may lead to artificial instabilities and, eventually, yield spurious oscillations and chaotic behavior by period-doubling bifurcations. This study extends these previous investigations to consider dispersed two-phase flow laden with solid particles, which can be heavier or lighter than the fluid in which they are immersed. The main result is that the numerical techniques applied to integrate the particle or bubble equation of motion are stable in the case of heavy particles but must be used very carefully when applied to bubbles or light solid particles in a fluid. During the analysis process, criteria have been established for choosing optimal time steps to simultaneously avoid numerical instabilities and guarantee code efficiency. © 2005 American Institute of Chemical Engineers AIChE J, 2006