  A class of supersymmetric (BPS saturated), static, spherically symmetric
solutions of four-dimensional effective N=4 supersymmetric superstring vacua,
which become massless at special points of moduli space, is studied in terms of
the fields of the effective heterotic string theory compactified on a
six-torus. Those are singular four-dimensional solutions corresponding to
$O(6,22,Z)$ orbits of dyonic configurations (with zero axion), whose
left-moving as well as right-moving electric and magnetic charges are
orthogonal (light-like in the $O(6,22,Z)$ sense), while the $O(6,22,Z)$ norms
of both the electric and magnetic charges are negative. Purely electric [or
purely magnetic] and dyonic configurations preserve $1\over 2$ and $1\over 4$
of N=4 supersymmetry, respectively, thus belonging to the vector and the
highest spin $3\over 2$ supermultiplets, respectively. Purely electric [or
purely magnetic] solutions (along with an infinite tower of $SL(2,Z)$
transformed states) become massless at a point of the corresponding
``one-torus'', thus may contribute to the enhancement of non-Abelian gauge
symmetry, while dyonic solutions become simultaneously massless at a point of
the corresponding two-torus, and thus may in addition contribute to the
enhancement of the local supersymmetry there.
