  Novel fundamental notions helping in the interpretation of the complex
dynamics of nonlinear systems are essential to our understanding and ability to
exploit them. In this work we predict and demonstrate experimentally a
fundamental property of Kerr-nonlinear media, which we name mode rejection and
takes place when two intense counter-propagating beams interact in a multimode
waveguide. In stark contrast to mode attraction phenomena, mode rejection leads
to the selective suppression of a spatial mode in the forward beam, which is
controlled via the counter-propagating backward beam. Starting from this
observation we generalise the ideas of attraction and rejection in nonlinear
multimode systems of arbitrary dimension, which paves the way towards a more
general idea of all-optical mode control. These ideas represent universal tools
to explore novel dynamics and applications in a variety of optical and
non-optical nonlinear systems. Coherent beam combination in
polarization-maintaining multicore fibres is demonstrated as example.
