This paper concerns the generalizability of biometric identification results from small-sized closed systems to larger open systems. Many researchers have claimed high identification accuracies on closed system consisting of a few hundred or thousand members. Here, we consider what happens to these closed identification systems as they are opened to non-members. We claim that these systems do not generalize well as the non-member population increases. To support this claim, we present experimental results on writer and iris biometric databases using Support Vector Machine (SVM) and Nearest Neighbor (NN) classifiers. We find that system security (1-FAR) decreases rapidly for closed systems when they are tested in open-system mode as the number of non members tested increases. We also find that, although systems can be trained for greater closed-system security using SVM rather than NN classifiers, the NN classifiers are better for generalizing to open systems due to their superior capab...