On-axis and vicinal 4H- and 6H-SiC(0001) surfaces have been investigated using atomic force microscopy and cross-sectional high-resolution transmission electron microscopy. We observed one-dimensionally ordered SiC surface nanostructures, which were energetically induced by self-ordering of nano-facets on any surfaces, regardless of polytypes and vicinal angles, after gas etching at high temperature. Two facet planes were typically revealed; (0001) and high index (11 (2) over barn) that are formed by equilibrium surface phase separation. A (11 (2) over barn) surface may have a free energy minimum due to attractive step-step interactions.