  The conifold singularities in the type-II string are considered as the points
of phase transition. In some cases, these singularities can be understood in
the framework of the conventional fields theores as the points of enhanced
gauge symmetry. We consider a class of three moduli Type-II strings. It is
shown the periods can be written in the form of hypergeometric series around
the singular points in these models. The leading expansion around the conifold
locus turns out to be described by Appell functions. In one singular point, we
observe the enhanced gauge symmetry of $SU(2)\times SU(2)$ independent of the
models. Around another conifold locus, however, the resulting expression of the
Appell functions depends on the models. We examine the result by considering a
relation between these Appell functions and underlying Riemann surfaces.
