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