Science in the former Soviet republics has not been insulated from the economic problems afflicting the entire state sector of the republic's economies. Funding cuts have given rise to a debate on phenomena not experienced by the "Soviet" science community in the past. One such phenomenon particularly, the emigration of scientists from the former Soviet Union, has attracted a great deal of attention in Russia as well as in the West. The author uses 1992 surveys of Russian aerospace and nuclear specialists and of Russian physicists to estimate that some 7,500 to 9,000 of "Soviet" physicists and mathematicians will leave the former Soviet Union. However, the likely composition of the outflow rather than its magnitude appears to be the problem, since, as surveys show, the best of the young generation of Russian scientists are the most likely candidates for emigration. This may be detrimental to the future of Russian science. From the point of view of the West, the scenario of Russian weapons specialists going to "problem" countries is the greatest risk associated with the emergent emigration of highly qualified specialists from Russia.