Alternating Phase Shift Masks (alt.PSM) became one of the primary options to keep optical lithography on its fast shrinking path. They promise -- and demonstrated by numerous examples -- lithography with k1 factors down to 0.25, which is equivalent to print structures below 100 nm using established DUV exposure tools. However, lithography at that small k1 factors is a highly non-linear process. So proximity effects are expected, when realistic chip structures have to be printed. In addition to the well-known proximity effects at the use of conventional chromium masks or half-tone phase shift masks, the width of a line printed by an alt.PSM depends also on the geometry of the surrounding phase shifters. The paper confirms, that a simulation-based OPC-tool is able to describe this effect correctly and to correct for it. However, experimental data and simulation results suggest, that there is an additional proximity effect arising from the 3- dimensional geometry of the phase edges. This proximity effect changes the effective phase of a given phase edge from its intended value. It is possible to correct this effect for one geometry, but for arbitrary geometries, phase changes as function of the proximity of phase edges must be taken into account. Based on simulation results of 3-dimensional alt.PSM geometries, we developed a strategy to include all proximity effects of alt.PSM in order to print realistic chip layouts with design rules down to 130 nm.