New kind of heavy-ion resonances recently discovered in nuclear collisions of 12 C+ 12 C and 16 O+ 16 O systems leading to various multi-cluster exit channels, such as 12 C+ 12 C →3α+ 12 C, 3α+3α, 2α+ 16 O and 16 O+ 16 O → (α+ 12 C)+ 16 O, (α+ 12 C)+(α+ 12 C), are studied theoretically by the coupled-channel (CC) and coupled-channel Born approximation (CCBA) calculations using microscopic cluster-model wave functions of the colliding nuclei, 12 C and 16 O, and the nucleus-nucleus interactions based on the realistic G-matrix interaction. These resonance states correspond to highly excited states of the compound systems, 24 Mg and 32 S nuclei, at excitation energies more than 40∼55 MeV, having the associated multi-cluster structures and large decay widths to these reaction channels. In this talk, we show that characteristic features of these newly-found resonances as well as those of the classical resonances of di-nucleus molecular nature are well reproduced by the microscopic CC and CCBA calculations. The reaction mechanism leading to the formation of these exotic resonances is also discussed in some detail for the 16 O+ 16 O → (α+ 12 C)+ 16 O, (α+ 12 C)+(α+ 12 C) and 12 C+ 12 C → 8 Be+ 16 O reactions. by guest on March 30, 2015 http://ptps.oxfordjournals.org/ Downloaded from a) The 1st decade, 1960s: Discovery of heavy-ion resonances Historically, such a di-nuclear structure was first observed 3) as sharp resonances in the 12 C+ 12 C collision at Coulomb-barrier energies around E c.m. 6 MeV, which by guest on March 30, 2015 http://ptps.oxfordjournals.org/ Downloaded from by guest on March 30, 2015 http://ptps.oxfordjournals.org/ Downloaded from