This paper examines the behavior of stochastically dependent serial and parallel processing models in the setting of a 2x2 factorial experiment. Interactions found in factorial experiments can provide insight into the underlying mental architecture operating in a given psychological task. Recent theoretical results classify serial vs. parallel (Townsend and Ashby, 1983; Townsend, 1984) and more complex networks (Schweickert, 1978; Townsend and Schweickert, 1985, 1989; Schweickert and Townsend, 1989) according to the types of factorial interaction they predict when selectivity of the factors is assumed. However, when one allows this selectivity to break down through a stochastic dependency between processes, other features of identifiability can result. One of these, which we term a single factor reversal of mean processing times, arises as a result of a negative dependence under certain circumstances. A theoretical analysis of the necessary and sufficient conditions for this reversal is given. Another characteristic of dependent systems that may contribute to their identifiability is that the interactions can be subadditive for some levels of the factors and superadditive at other levels. This change in contrast is not possible for independent serial and parallel models. The relationships of contrast, dependence, and single factor reversals are explored.