In a typical redundant target experiment, participants receive either unimodal of bimodal redundant signals from different modalities. A well known finding is that responses for bimodal stimuli are substantially faster than for unimodal stimuli (redundant signals effect, RSE). I present a stochastic model of the RSE (diffusion superposition model, DSM, Schwarz, 1994, 2006) which allows nearly perfect prediction of the mean and variance of response times in auditory-visual stimuli with different onset asynchrony. The basic integration mechanism in the DSM is a linear superposition of neural signals. In three experiments, the basic RSE paradigm was extended to include simple, go/nogo, and choice responses (Exp. 1), spatial attention (Exp. 2), and judgements of temporal order (Exp. 3). In all experiments, the model prediction was excellent, underlining the role of additive neural interactions in audiovisual integration.