We demonstrate a "coarse time-stepper" based approach for the extraction of continuum-level stability and bifurcation information from kinetic theory based, LB simulations. Acting directly on the LB simulator, we sidestep the necessity of deriving macroscopic, explicitly closed continuum conservation equations. The approach is used to analyze the dynamics and the oscillatory instability of two-dimensional periodic arrays of gas bubbles rising in a liquid. (C) 2004 Elsevier Ltd. All rights reserved.