In the human sciences, a common assumption is that latent traits have a hierarchical structure. Higher order item response theory models have been developed to account for this hierarchy. In this study, computerized adaptive testing (CAT) algorithms based on these kinds of models were implemented, and their performance under a variety of situations was examined using simulations. The results showed that the CAT algorithms were very effective. The progressive method for item selection, the Sympson and Hetter method with online and freeze procedure for item exposure control, and the multinomial model for content balancing can simultaneously maintain good measurement precision, item exposure control, content balance, test security, and pool usage. (Contains 3 tables and 2 figures.)