[en] The SuperLEAR project consists of a dedicated high current p-bar ring at CERN. It is proposed to search for the missing cc-bar charmonium states and for exotic charmonium states containing a valence gluon (cc-barg hybrids) by measuring their excitation as a function of p-bar momentum, specifically p-barp→cc-barg→mesons, in exclusive final states which contain either J/Ψ (→e⁺e^-) or η_c (→γγ) associated with one or several mesons (π⁰, η, η', ω), and leading to several detected photons. It is also proposed to search for new varieties of exotic light mesons (glueballs, hybrids and multiquark states) in the rather unexplored 2-3 GeV mass range by studying p-barp annihilation at a fixed p-bar momentum into exclusive final states involving neutral mesons (η, η', ω) and leading also to several detected photons. (author) 62 refs.; 4 figs.; 2 tabs