In this paper, an equivalence condition for deciding whether a default theory isan auto-compatible default one is presented. Under the condition, the existence of extension of anauto-compatible default theory is a natural result. By introducing a well-ordering over the set D ofdefault rules, the extensions of an auto-compatible default theory (D, W) can be computed directly.The condition represents clearly the characterization of an auto-compatible default theory, andsome properties about auto-compatible default theory, such as semi-monotonicity, become naturalcorollaries. Based on the characterization, the revision of default beliefs is discussed to ensure theexistence of extension of the default theory, and the method is applied to investigate stable modelsof a general logic program.