  We consider the singular phases of the smooth finite-gap integrable systems
arising in the context of Seiberg-Witten theory. These degenerate limits
correspond to the weak and strong coupling regimes of SUSY gauge theories. The
spectral curves in such limits acquire simpler forms: in most cases they become
rational, and the corresponding expressions for coupling constants and
superpotentials can be computed explicitly. We verify that in accordance with
the computations from quantum field theory, the weak-coupling limit gives rise
to precisely the "trigonometric" family of Calogero-Moser and open Toda models,
while the strong-coupling limit corresponds to the solitonic degenerations of
the finite-gap solutions. The formulae arising provide some new insights into
the corresponding phenomena in SUSY gauge theories. Some open conjectures have
been proven.
