Simulated data were used to demonstrate that groups formed by imposing cut-points based on either discrepancy or low-achievement definitions of learning disabilities (LD) are unstable over time. Similar problems were demonstrated in longitudinal data from the Connecticut Longitudinal Study, where 39% of the children designated as having LD in Grade 3 changed group placement with repeated testing in Grade 5. These results show that the practice of subdividing a normal distribution with arbitrary cut-points leads to instability in group membership. Approaches to the identification of children as having LD based solely on individual test scores not linked to specific behavioral criteria lead to invalid decisions about individual children. Low-achievement definitions are not a viable alternative to IQ-discrepancy definitions in the absence of other criteria, such as the traditional exclusions and response to quality intervention. If we accept the premise of multiple classes of low achievers, then we must develop identification systems that are valid and abandon systems whose only merits are their historical precedence and convenience.