  The two matrix model is considered, with measure given by the exponential of
a sum of polynomials in two different variables. It is shown how to derive a
sequence of pairs of ``dual'' finite size systems of ODEs for the corresponding
biorthonormal polynomials. An inverse theorem is proved showing how to
reconstruct such measures from pairs of semi-infinite finite band matrices
defining the recursion relations and satisfying the string equation. A proof is
given in the $N\to \infty$ limit that the dual systems obtained share the same
spectral curve.
