  The BPS-spectrum is known to change when moduli cross a wall of marginal
stability. This paper tests the compatibility of wall-crossing with S-duality
and electric-magnetic duality for N=2 supergravity. To this end, the
BPS-spectrum of D4-D2-D0 branes is analyzed in the large volume limit of
Calabi-Yau moduli space. Partition functions are presented, which capture the
stability of BPS-states corresponding to two constituents with primitive
charges and supported on very ample divisors in a compact Calabi-Yau. These
functions are `mock modular invariant' and therefore confirm S-duality.
Furthermore, wall-crossing preserves electric-magnetic duality, but is shown to
break the `spectral flow' symmetry of the N=(4,0) CFT, which captures the
degrees of freedom of a single constituent.
