  We present axion-dilaton black-hole and multi-black-hole solutions of the
low-energy string effective action. Under $SL(2,R)$ electric-magnetic duality
rotations only the ``hair" (charges and asymptotic values of the fields) of our
solutions is transformed. The functional form of the solutions is
duality-invariant. Axion-dilaton black holes with zero entropy and zero area of
the horizon form a family of stable particle-like objects, which we call {\it
holons}. We study the quantization of the charges of these objects and its
compatibility with duality symmetry. In general the spectrum of black-hole
solutions with quantized charges is not invariant under $SL(2,R)$ but only
under $SL(2,Z)$ or one of its subgroups $\Gamma_{l}$. Because of their
transformation properties, the asymptotic value of the axion-dilaton field of a
black hole may be associated with the modular parameter $\tau$ of some complex
torus and the integer numbers $(n,m)$ that label its quantized electric and
magnetic charges may be associated with winding numbers.
