Equating a test form to itself through a chain of equatings, commonly referred to as circular equating, has been widely used as a criterion to evaluate the adequacy of equating. This paper uses both analytical methods and simulation methods to show that this criterion is in general invalid in serving this purpose. For the random groups design done in the same year, it is shown analytically that circular equating will always result in the identity function (i.e., the perfect result) even with the presence of random and systematic equating errors. For the random groups design done in the different years, a heuristic argument is provided that circular equating will generally deviate from the identity function by some random sampling error. A simulation study for this design also showed that the expected values of the circular equating may deviate slightly from the identity function but those deviations do not reflect the systematic error (bias) embedded in the equating. For the common-item nonequivalent groups design, a simulation study was done to show that circular equating again can not reflect the systematic error in equating. More effective ways of assessing random and systematic equating errors are recommended. (Contains 4 tables, 4 figures, and 13 references.) (Author)