The authors present a theory of stochastic interactive parallel processing with special emphasis on channel interactions and their relation to system capacity. The approach is based both on linear systems theory augmented with stochastic elements and decisional operators and on a metatheory of parallel channels' dependencies that incorporates standard independent and coactive parallel models as special cases. The metatheory is applied to OR and AND experimental paradigms, and the authors establish new theorems relating response time performance in these designs to earlier and novel issues. One notable outcome is the remarkable processing efficiency associated with linear parallel-channel systems that include mutually positive interactions. The results may offer insight into perceptual and cognitive configural-holistic processing systems.