We report on the nonlinear rheology of a reversible supramolecular polymer based on hydrogen bonding. The coupling between the flow-induced chain alignment and breakage and recombination of bonds between monomers leads to a very unusual flow behavior. Measured velocity profiles indicate three different shear-banding regimes upon increasing shear rate, each with different characteristics. While the first of these regimes has features of a mechanical instability, the second shear-banding regime is related to a shear-induced phase separation and the appearance of birefringent textures. The shear-induced phase itself becomes unstable at very high shear rates, giving rise to a third banding regime. DOI: 10.1103/PhysRevLett.97.108301 PACS numbers: 83.60.Rs, 47.50.ÿd, 83.60.Wc, 83.80.Rs Coupling between fluid microstucture and flow yields a rich scala of non-Newtonian behavior in complex fluids. Many complex fluids display flow instabilities or flowinduced phase transitions above a critical shear rate or stress. Solutions of wormlike micelles, for example, undergo a shear-banding instability in which the fluid separates in the gradient direction into coexisting regions (bands) supporting different shear rates (''gradient banding'') [1,2]. Rod-like colloids, on the other hand, display ''vorticity banding,'' in which the different shear bands are separated in the vorticity direction [3]. Several other systems, such as attractive emulsions or carbon nanotube suspensions, show an elastic instability that leads to the formation of shear-induced aggregates aligned in the vorticity direction [4,5].Several aspects of these instabilities can be reproduced by phenomenological models, see e.g. [6]. Shear banding in the gradient direction, for example, can be related to a nonmonotonic constitutive equation relating the shear stress and the shear rate _ . When a shear rate is applied in the region where decreases with _ , an initially homogeneous flow becomes mechanically unstable. In the simplest scenario, the system then separates into a weakly sheared band that flows at _ 1 and a highly sheared band that flows at _ 2 [1]. Increasing the overall shear rate within the unstable region leads to an increase of the width of the high shear band, while the stress remains constant. The microscopic origin of the shear-banding instability varies for different systems. For wormlike micelles, two alternative mechanisms for shear banding have been proposed. Cates and coworkers predicted a nonmonotonic constitutive equation leading to a shear-banding instability, based on the Doi and Edwards reptation model for polymers [1]. This purely mechanical instability is responsible for shear banding in semidilute solutions of wormlike micelles, far from an equilibrium phase transition [2]. In more concentrated systems, on the other hand, the appearance of a banded flow is related to a first-order phase transition induced by the flow, such as an isotropic-to-nematic transition [6,7]. In this case, the two shear bands correspond to two structurally ...