The output intensity of a hybrid bistable system with a delay in the feedback loop is known to undergo regular and irregular self-pulishg. With the help of high-resolutin power spectra, we have analyzed numerically the transition of this system into chaos for several different valus of the delay thime, and found evidence for the exzistence of an infinite sequence of period-doubling bifurcations. followed by a reverse sequence in which the periodic components of the spectrum are supperimposed to a continuous noisy structure. We jave stidoed tje effect pf extermal Gaussian random noise and verified, as expected, the occurrence of bifurcation gaps. In the vicinity of the self-pulising threshold, more than three independent frequency components coexist without evidence for the appearance of a strange attractor.