Electromagnetic instability of uniform current flow in anisotropic type-11 superconductors has been considered. It is shown that the instability occurs in the region j(f1) < j < j(f2), essentially depending on the orientation of the current density j with respect to the symmetry axes. This is due to the coupling of the anisotropy and strong nonlinearity of the I-V curve in the flux-creep regime, regardless of specific mechanisms of flux dynamics. Peculiarities of the instability in different models of resistive states (conventional flux-creep model, vortex glass, critical-state model, etc.) are examined. The instability is shown to destroy laminar current configurations and is accompanied by the appearance of current domain walls and macroscopic-vortex current patterns, which depend on the sample geometry. A qualitative description of the macroscopic vortex structures is given, and their manifestations in electric and magnetic properties of anisotropic superconductors are discussed.