Models of two-phase flow and displacement in porous media developed so far typically involve one displacing (invader) and one displaced (defender) fluid. However, in many important applications of these phenomena at field scales, such as two-phase flow in fractured porous media, as well as in laboratory studies, require at least two invaders which also act as the defenders. The results of extensive Monte Carlo simulations of a novel model of such phenomena are reported. The porous medium is represented as a network of pore throats and pore bodies to which effective sizes are assigned that are selected from a given distribution. Both 2-D and 3-D networks are used. The simulation results indicate that the structure of the fluids' clusters is volatile, that is, it changes with the time t and length scale. Moreover, ns (s, t), the number of fluid clusters of size s, 〈s(t)〉, the mean cluster size, and S(t), the saturation of the fluids all vary with t in a manner that resembles an oscillatory behavior. This behavior is caused by the dynamic breakup and recoalescence of the fluids' clusters, which is a result of simultaneous invasion of the two fluids. The flow effect of thin wetting fluid films on the dynamics of the displacement is strong over a broad range of the capillary number. Novel dynamical scaling laws for the cluster-size distribution are obtained. Some results agree qualitatively with the experimental observations, while others provide rational explanations for some unexplained data.