In this paper we study some asymptotics for solutions of the Ginzburg-Landau equations with Dirichlet boundary conditions. We consider the solutions ( $u_{in}$, $A_{in}$) which minimize the Ginzburg-Landau energy functional $E_{in}$(u, A). We show that the solutions ( $u_{in$}$ , $A_{in}$) converge to some ( $u_{*}$, $A_{*}$) in various norms as the coupling parameter $in$longrightarrow0.ow0.