  We construct generating solutions for general D-dimensional ($4 \le D \le 9$)
rotating, electrically charged, black holes in the effective action of
toroidally compactified heterotic (or Type IIA) string. The generating solution
is parameterized by the ADM mass, two electric charges and $[{D-1}\over 2]$
angular momenta (as well as the asymptotic values of one toroidal modulus and
the dilaton field). For $D \ge 6$, those are generating solutions for {\it
general} black holes in toroidally compactified heterotic (or type IIA) string.
Since in the BPS-limit (extreme limit) these solutions have singular horizons
or naked singularities, we address the near extreme solutions with all the
angular momenta small enough. In this limit, the thermodynamic entropy can be
cast in a suggestive form, which has a qualitative interpretation as
microscopic entropy of (near)-BPS-saturated charged string states of toroidally
compactified heterotic string, whose target-space angular momenta are
identified as $[{{D-1}\over 2}]$ U(1) left-moving world-sheet currents.
