The structures of Ωω states with spin-parity J=5/2~-,3/2~-,and 1/2~- are dynamically studied in boththe chiral SU(3)quark model and the extended chiral SU(3)quark model by solving a resonating group method(RGM)equation.The model parameters are taken from our previous work,which gave a satisfactory description of the energiesof the baryon ground states,the binding energy of the deuteron,the nucleon-nucleon(NN)scattering phase shifts,andthe hyperon-nucleon(YN)cross sections.The calculated results show that the Ωω state has an attractive interaction,and in the extended chiral SU(3) quark model such attraction can make for a Ωω quasi-bound state with spin-parityJ~ρ=3/2~- or 5/2~- and the binding energy of about several MeV.