Degenerate critical points on a 2-compnent reaction diffusion system with a global inhibition (GI) are studied. They can be an organizing center for a variety of spatially non-uniform oscillations. The Hopf-bifurcation point for the 0-mode oscillation (spatially uniform oscillation) is controlled by the
strength of GI so that the eairlier destabilization of the higher mode oscillations can happen.