BLACK-HOLES AND ELEMENTARY STRING STATES IN N=2 SUPERSYMMETRIC STRINGTHEORIES

We compare the logarithm of the degeneracy of BPS saturated elementary string states and the string modified Bekenstein-Hawking entropy of t he corresponding black holes in N = 2 supersymmetric heterotic string compactification to four dimensions. As in the case of N = 4 supersymm etric theory, the two results match up to an overall undetermined nume rical factor. We also show that this undetermined numerical constant i s identical in the N = 2 and N = 4 supersymmetric theories, therby sho wing that the agreement between the Bekenstein-Hawking entropy and the microscopic entropy for N = 2 theories does not require any new ident ity, other than the one already required for the N = 4 theory. A simil ar result holds for type II string compactification as well.