This volume is the second part of a Report of the Survey Committee of the Conference Board of the Mathematical Sciences, and presents data on a number of specific conditions and problems regarding the broad subject of graduate education in the mathematical sciences. Volume I, ASPECTS OF UNDERGRADUATE TRAINING IN THE MATHEMATICAL SCIENCES, discusses the origins and purposes of the committee; Volume III will contain recommendations pertaining to the future collection and dissemination of data on both graduate and undergraduate work in the mathematical sciences. Information was gathered from 3 sources: a graduate questionnaire sent by the conference Board to all PhD-granting mathematical science departments during the 1966-67 school year; departmental applications for National Science Foundation Traineeships; and the Doctoral Records File maintained by the National Academy of Sciences. Six basic topics are discussed: background information; graduate faculty; graduate students; the process of graduate education; a study of thesis supervision; and post-doctoral employment and research. Within these topics, 4 areas of the mathematical sciences are included: pure mathematics, applied mathematics, statistics, and computer science. Extensive use is made of tables and figures, which often interrelated the American Council of Education departmental quality ratings (Cartter Report) with other variables. Inferences are drawn from the information presented, but no recommendations for improvement are made. (DS)