Three apperception theories that explain how people respond to Thematic Apperception Test cards are proposed: a simple apperception theory, an apperception theory with a dynamic component, and an apperception theory with 2 types of responses. Each theory is translated into an item response theory model and is applied to need for achievement (nAch) data. The analysis indicates that the best fitting model is provided by the apperception theory with 2 types of responses, also referred to as the drop-out apperception theory. The 1st type of response predicted by this theory is determined by the nAch level of the person and the achievement-response-eliciting value of the card; this response is diagnostic for the nAch level of the person. The 2nd type of response is not determined by the 2 aforementioned characteristics and is therefore not diagnostic of the person's nAch level. The results are cross-validated for need for power and need for affiliation.