Same basic properties of resonators from a wave – optical and from a ray resonator were investigated. These properties play a pivoted role in determining both the spectral properties of optical resonators and the behavior of rays inside such resonators. In this investigation, the phase was used as a unifying concept. Furthermore the basic expressions for paraxial two mirror resonators were considered a long with a special case where the phase assumes a rational value=2 k N. In this case a paraxial two-mirror resonator has, at the same time, a highly degenerate eign frequency spectrum and supports closed periodic orbits that repeat after N round trips. Outside the paraxial limit, these periodic orbits are still useful they allow us to make general statements about the behavior of the phase for non paraxial eign modes. Also extend the expressions for the paraxial two-mirror resonator so that can be used to analyse paraxial resonators with astigmatic eign modes. Also, I suggest a possible application of a degenerate two-mirror resonator as a high- resolution length- sensing interferometer. I discuss its principle of operation and point out some limitations.