Today the scientific potential of any country, its science cadres, the volume and scale of the research being conducted, the number of science centers, the quality and subject matter of the research, the level of the material and technical equipment of its research laboratories, and other aspects constitute a most important factor in ensuring national security. How are the most urgent problems of science cadre training addressed in Russia and other countries? What difficulties are experienced by young scientists as they begin their career in science? This study presents an analysis in a comparison format of the practice of science cadre training in Russia and the United States. In examining the American experience of training doctoral students, use is made of materials published in "The Chronicle of Higher Education" in 2007 and 2008, in particular, facts presented in R. Monastersky's article "The Real Science Crisis: Bleak Prospects for Young Researchers." On the Russian side, these scientists agreed to take part in the discussions: (1) Professor G.A. Bokareva, a doctor of pedagogical sciences and chairperson of the dissertation council at BGARF (Baltic State Academy of the Fishing Fleet) with the specialty of "The Theory and Methodology of Professional Education"; (2) Professor M.I. Rozhkov, a doctor of pedagogical sciences and director of the Institute of Pedagogy and Psychology at the Iaroslavl K.D. Ushinskii State Pedagogical University; (3) Professor V.V. Briukhanov, a doctor of physical and mathematical sciences and vice rector for science work at Kaliningrad State Technical University; and (4) Professor G.M. Fedorov, a doctor of geographical sciences and vice rector for science work at the Russian I. Kant State University. The conversation was arranged in the following form: authors presented the results of a study they had conducted, indicating a number of problems in science cadre training practices in the United States, and then their Russian colleagues commented. [This article was translated by Kim Braithwaite.] (Contains 1 note.)