I present the idea underlying the experiments on molecules to test the validity of the symmetrization postulate of quantum mechanics and the spin-statistics connection for nuclei. I describe in some detail recent experiments onO2andCO2molecules and show that these should be considered as tests of the spin-statistics connection for the spin-0 oxygen nuclei. I discuss the possibility of new experiments to test the spin-statistics connection and the symmetrization postulate. ©2000 American Institute of Physics.