The Bonnor beam can be generalized to several parallel beams travelling in the same direction. Perhaps surprisingly, the beams do not curve toward one another. On the other hand, "anti-parallel" beams (travelling along parallel trajectories, but in opposite directions) do attract each other. This reflects a general phenomenon: two pp-waves with parallel wave vectors superimpose linearly, but pp-waves with nonparallel wave vectors (including antiparallel Bonnor beams) do not superimpose linearly, as we would expect from the nonlinear nature of the Einstein field equation.