The area under the receiver operating characteristic (ROC) curve, AUC, is commonly used to assess the ability of a diagnostic test to correctly classify individuals into diseased and nondiseased populations. When there are two diagnostic tests available, it is of interest to evaluate and compare their performances. Based on the difference of two placement values, we propose a two-sample empirical likelihood method for comparing AUCs of two ROC curves. The proposed empirical likelihood ratio statistic converges in distribution to a scaled chi-squared random variable. Simulation results show that the proposed empirical likelihood method has better finite-sample performance than other competitors.