That speakers can vary their speaking rate is evident, but how they accomplish this has hardly been studied. Consider this analogy: When walking, speed can be continuously increased, within limits, but to speed up further, humans must run. Are there multiple qualitatively distinct speech “gaits” that resemble walking and running? Or is control achieved by continuous modulation of a single gait? This study investigates these possibilities through simulations of a new connectionist computational model of the cognitive process of speech production, EPONA, that borrows from Dell, Burger, and Svec’s (1997) model. The model has parameters that can be adjusted to fit the temporal characteristics of speech at different speaking rates. We trained the model on a corpus of disyllabic Dutch words produced at different speaking rates. During training, different clusters of parameter values (regimes) were identified for different speaking rates. In a 1-gait system, the regimes used to achieve fast and slow speech are qualitatively similar, but quantitatively different. In a multiple gait system, there is no linear relationship between the parameter settings associated with each gait, resulting in an abrupt shift in parameter values to move from speaking slowly to speaking fast. After training, the model achieved good fits in all three speaking rates. The parameter settings associated with each speaking rate were not linearly related, suggesting the presence of cognitive gaits. Thus, we provide the first computationally explicit account of the ability to modulate the speech production system to achieve different speaking styles.