  We present string-theory derivation of the semiclassical entropy of extremal
dyonic black holes in the approach based on conformal sigma model (NS-NS
embedding of the classical solution). We demonstrate (resolving some puzzles
existed in previous related discussions) that the degeneracy responsible for
the entropy is due to string oscillations in four transverse dimensions
`intrinsic' to black hole: four non-compact directions of the D=5 black hole
and three non-compact and one compact (responsible for embedding of magnetic
charges) dimensions in the D=4 black hole case. Oscillations in other compact
internal dimensions give subleading contributions to statistical entropy in the
limit when all charges are large. The dominant term in the statistical entropy
is thus universal (i.e. is the same in type II and heterotic string theory) and
agrees with Bekenstein-Hawking expression.
