In conclusion we have pointed out the existence of a strongly correlated regime in quasi-1D Bose gases beyond the Tonks-Giradeau regime. This regime can be entered by exploiting a confinement induced resonance of the effective 1D scattering amplitude. We calculate the equation of state of the gas in the super-Tonks regime using VMC and we estimate the critical density for the onset of instability against cluster formation. The static structure factor and one-body density matrix are calculated exactly within the hard-rod model, which provides the correct description of the system for small values of the gas parameter. For harmonically trapped systems we provide explicit predictions for the frequency of the lowest compressional mode.