Modern experimental techniques based on collinear laser spectroscopy have led to greatly improved versions of the classical Ives-Stilwell experiment. The new experiments employ collinear laser beams and measure the Doppler shift as it is seen in the rest frame of a relativistic particle beam. This note analyzes these experiments in the framework of a test theory of special relativity due to Mansouri and Sexl. It is found that the experiments can test the coefficient functiona(υ2 (responsible for time dilation), but are insensitive tob,d andɛ. While the Mansouri-Sexl theory in principle allows for an anisotropy of the velocity of light with respect to a moving reference frame, anisotropy effects cancel out in Ives-Stilwell type experiments. These experiments by themselves are not sufficient for a direct observation of such an anisotropy.