The performances of 124 physics graduate students in two departments have been compared with their Graduate Record Examination scores. It is indicated that the currently used forms of the Advanced Physics Test and the Quantitative Aptitude Test are satisfactory devices for predicting a meaningful probability that a student will be a successful candidate for the doctorate. Both tests, however, fail to distinguish among “fair,” “good,” and “excellent,” students. The GRE scores furnish information of significance for the admission of students to graduate departments but they cannot be counted upon to determine which students show highest promise or to which a limited number of fellowships or other financial aids should be awarded.