  We formulate supersymmetric low energy dynamics for BPS dyons in
strongly-coupled N=2 Seiberg-Witten theories, and derive wall-crossing formulae
thereof. For BPS states made up of a heavy core state and n probe (halo) dyons
around it, we derive a reliable supersymmetric moduli dynamics with 3n bosonic
coordinates and 4n fermionic superpartners. Attractive interactions are
captured via a set of supersymmetric potential terms, whose detail depends only
on the charges and the special Kaehler data of the underlying N=2 theories. The
small parameters that control the approximation are not electric couplings but
the mass ratio between the core and the probe, as well as the distance to the
marginal stability wall where the central charges of the probe and of the core
align. Quantizing the dynamics, we construct BPS bound states and derive the
primitive and the semi-primitive wall-crossing formulae from the first
principle. We speculate on applications to line operators and Darboux
coordinates, and also about extension to supergravity setting.
