  There is a close relation between duality in $N=2$ SUSY gauge theories and
integrable models. In particular, the quantum moduli space of vacua of $N=2$
SUSY $SU(3)$ gauge theories coupled to two flavors of massless quarks in the
fundamental representation can be related to the spectral curve of the
Goryachev-Chaplygin top. Generalizing this to the cases with {\it massive}
quarks, and $N_f = 0,1,2$, we find a corresponding integrable system in seven
dimensional phase space where a hyperelliptic curve appears in the Painlev\'e
test. To understand the stringy origin of the integrability of these theories
we obtain exact nonperturbative point particle limit of type II string
compactified on a Calabi-Yau manifold, which gives the hyperelliptic curve of
$SU(2)$ QCD with $N_f =1$ hypermultiplet.
