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Precision measurements constitute only one facet of a sound high-energy-physics project for the future. They need to be complemented with direct searches for new phenomena at an energy-frontier facility, to possibly answer fundamental questions that will unavoidably arise from these precision measurements.   Both the $\epem$ Higgs factories discussed in Section~\ref{sec:Higgs} are accompanied by high-energy upgrade projects. For the ILC, it is foreseen to double its length to reach a centre-of-mass energy of 500 GeV, and it is not yet excluded to extend it by another factor of two towards $\sqrt{s} =$ 1 TeV. Another linear collider project, CLIC~\cite{cite:CLICDR}, could also take over for the high-energy physics programme all the way to $\sqrt{s}=$ 3 TeV. The foreseen upgrade of TLEP is of another, unique, nature. It would consist in re-using the 80-to-100 km tunnel for a very-large-energy large hadron collider (VHE-LHC}. (VHE-LHC).  If instrumented with magnets of 16 T, pp collisions would be produced at a centre-of-mass energy of 80 to 100 TeV.