Nonparametric item response models have been developed as alternatives to the relatively inflexible parametric item response models. An open question is whether it is possible and practical to administer computerized adaptive testing with nonparametric models. This paper explores the possibility of computerized adaptive testing when using nonparametric item response models. A central issue is that the derivatives of item characteristic curves may not be estimated well, which eliminates the availability of the standard maximum Fisher information criterion. As alternatives, procedures based on Shannon entropy and Kullback-Leibler information are proposed. For a long test, these procedures, which do not require the derivatives of the item characteristic curves, become equivalent to the maximum Fisher information criterion. A simulation study is conducted to study the behavior of these two procedures, compared with random item selection. The study shows that the procedures based on Shannon entropy and Kullback-Leibler information perform similarly in terms of root mean square error, and perform much better than random item selection. The study also shows that item exposure rates need to be addressed for these methods to be practical.