  We consider the normalized Ricci flow $\del_t g = (\rho - R)g$ with initial
condition a complete metric $g_0$ on an open surface $M$ where $M$ is conformal
to a punctured compact Riemann surface and $g_0$ has ends which are asymptotic
to hyperbolic cusps. We prove that when $\chi(M) < 0$ and $\rho < 0$, the flow
$g(t)$ converges exponentially to the unique complete metric of constant Gauss
curvature $\rho$ in the conformal class.
