Braided rivers produce flow confluences and divergences (diffluences) in roughly equal numbers, but braided river research has focused mainly on confluences. Divergences, however, are of equal importance dynamically: they are sites of formation of central bars and the development of flow divisions that can steer the flow toward one part of the braided network or another. In a series of experiments on flow in isolated, well-defined bifurcations, we found that although a central bar always develops, the divided flow may continue to flow on both sides of the bar (stable bifurcation) or may eventually be forced entirely to one side of the bar or the other (unstable bifurcation). We found that an unstable bifurcation forms when the flow field is characterized by both a low Shields stress and a nonuniform incoming flow. We also found that divergences with erodible banks tend to an equilibrium configuration that depends mainly on the widening ratio of the channel.