H-2 oxidation on Pt electrodes, a comparatively simple electrocatalytic reaction, has been known for a long time to exhibit a variety of complex temporal oscillations, depending on the composition of the supporting electrolyte. We report, on the one hand, recent observations of spatial instabilities in the bistable and oscillatory region in this system. The studies indicate that the spatio-temporal dynamic is by far richer than has been assumed so far. On the other hand, aperiodic responses of the system in cyclic voltammetric experiments are described. This behavior is similar to the one observed in potentiodynamic measurements during the electro-oxidation of small organic molecules. A possible common origin of all these complex, current-voltage responses is discussed.