Abstract: We consider the quantum dynamics of a single particle in the plane under the influence of a constant perpendicular magnetic and a crossed electric potential field. For a class of smooth and small potentials we prove that the Hamiltonian is unitarily equivalent to an effective Hamiltonian which commutes with the observable of kinetic energy. Further we discuss the derived quantum network percolation model suggested by Chalker and Coddington. For the restriction to a cylinder of perimeter 2M we prove simplicity of the Lyapunov exponents, finiteness of the localization length and compute the mean Lyapunov exponent by a Thouless formula.