  Unstable minimal surfaces are the unstable stationary points of the
Dirichlet-Integral. In order to obtain unstable solutions, the method of the
gradient flow together with the minimax-principle is generally used. The
application of this method for minimal surfaces in the Euclidean spacce was
presented in \cite{s3}. We extend this theory for obtaining unstable minimal
surfaces in Riemannian manifolds. In particular, we handle minimal surfaces of
annulus type, i.e. we prescribe two Jordan curves of class $C^3$ in a
Riemannian manifold and prove the existence of unstable minimal surfaces of
annulus type bounded by these curves.
