In this paper we propose a simple method for order determination based on a generalized adaptive law which is used to adjust parameters in adaptive systems. The paper first reveals certain properties of the law and shows how they can be utilized for order determination in specific algorithms obtained from the law. The method requires no modifications of the algorithms but merely uses some quantities obtained directly from the algorithms. It can exhibit satisfactory performance in the noise-free case. Like other methods, however, it degenerates as noise increases. This degeneration is overcome by enhancing the original method by a correlation technique. Detailed discussions on the enhanced method are given.