Molecular dynamics simulation studies were carried out on N-2- and O-2-hydrates to reveal distributions and intramolecular vibrational spectra of diatomic guest molecules in two different sized cages. It was found that the guest molecules in the large cages distribute apart from the centers and move around in the cages while those in the small cages are located al the centers and that the guest molecules in the small cages have a preferred orientation which lie on a crystallographic {111} plane. These two results are well explained in terms of the size difference of the two cages and the distortion of the small cages, respectively. Vibrational spectra calculated for the stretching modes of the guest molecules showed double maxima for those in the large cages and a single maximum for those in the small cages. No significant difference between nitrogen and oxygen was found in all behaviors examined, except double maxima in the vibrational spectra of oxygen even in small cages.