  The normal and the superconducting state of two coupled CuO_2 layers in the
High-T_c superconductors are investigated by using the bilayer Hubbard model,
the FLEX approximation on the real frequency axis and the Eliashberg theory. We
find that the planes are antiferromagnetically correlated which leads to a
strongly enhanced shadow band formation. Furthermore, the inter-layer hopping
is renormalized which causes a blocking of the quasi particle inter-plane
transfer for low doping concentrations. Finally, the superconducting order
parameter is found to have a d_{x^2-y^2} symmetry with significant additional
inter-layer contributions.
