High resolution laser techniques and high velocity resolution of particles in a storage ring will be combined to test the validity of special relativity. The relativistic Doppler shift experiments will test both the time dilation effect and the isotropy in the speed of light. The experiments are based on two photon spectroscopy, in which an atom makes a transition by simultaneously absorbing a photon from each of two laser beams, one traveling in and the other opposite to the direction of the atom. This allows internal cancellation of the classical first order Doppler shift, leaving the relativistic effects as the dominant term.