In psychological research it can be of interest to differentiate between the categorical (taxonic) vs dimensional (nontaxonic) nature of phenomena, for example in the field of psychopathology. For categorical (taxonic) structures a further differentiation is possible: between categorical structures with dimensional equivalence and a substantial main effect, and structures without dimensional equivalence (independent of the main effect). Previous taxometric studies have not concentrated in an explicit way on the case of nonequivalence. It is shown here that under favorable circumstances both types of categorical structures can be detected using the taxometric procedure L-Mode, but that they cannot be differentiated from one another.