Physics at a future collider beyond the LHC and a TeV class linear collider

After the LHC will have probed the physics at the TeV frontier, new generations of colliders capable of reaching into the multi-TeV energy domain will need to be considered. Concepts for both high energy e⁺e^- linear colliders and muon storage rings have been proposed as well as hadron colliders. Highly challenging R&D programs are presently pursued to demonstrate their principles.<br> The definition of a physics programme in the multi-TeV range still requires essential data that is likely to become available only after the first years of LHC operation and, possibly, also the results from a TeV-class linear collider. At present we have to envisage several possible scenarios for the fundamental questions to be addressed by collider experiments in the next decade, to guide the choices in the accelerator designs and parameters.<BR> After a brief review of the main accelerator projects and the present status of their R&D, I shall discuss the main signatures of the physics of possible relevance in relation to the experimental conditions offered by the different accelerators. Special attention will be devoted to comparisons to LEP and LHC, to verify to which extent the extrapolations of the experimental techniques successfully applied at LEP and presently developed for the LHC will still be applicable at multi-TeV colliders.