In this article, the author discusses and presents seven possibilities that describe how symmetry principles are reflected in behavior analysis. First, if there are apparently no functional distinctions to be made between positive and negative reinforcement, then reinforcer effectiveness (by various measures) is invariant under a simple inversion of procedure, for example, onset as opposed to offset of pertinent events. Second, the degree to which this applies to reinforcement should be extended to include positive and negative punishment. Third, there is some evidence that reinforcement and punishment are, in some sense, mirror images of each other and therefore another form of symmetry. Fourth, discrimination and generalization are in a virtually perfect symmetrical relation. Fifth, in a three-term contingency the antecedent stimulus, operant class, and reinforcing consequence possess a kind of circular symmetry in which none of the terms can stand alone, but have meaning only through their interaction; each, in some sense, controls the other. Sixth, in shaping behavior, one recognizes the symmetry between the behaviors of the shaper and the shapee. Seventh, just as the laws of physics do not depend on time or place, the laws of behavior appear to operate over an enormous range of species, a biological feature shared perhaps only with certain biochemical pathways. As a corollary to this invariance, behavior analysts often assume that principles of reinforcement apply not only to the behavior of individuals but to groups of individuals as well--a kind of scale invariance.