  We study the integral representation for the exact solution to
nonperturbative $c le 1$ string theory. A generic solution is determined by two
functions $W(x)$ and $Q(x)$ which behaive at infinity like $x^p$ and $x^q$
respectively. The integral model for arbitrary $(p,q)$ models is derived which
explicitely demonstrates $p-q$ duality of minimal models coupled to gravity. We
discuss also the exact solutions to string equation and reduction condition and
present several explicit examples.
