Resonance fluorescence of a driven Jaynes-Cummings system is studied theore
tically when the cavity is driven by a classical field of arbitrary strengt
h. In the regime of strong atom-cavity coupling, there occur anomalous reso
nance peaks at +/- root 2g',+/- root 3g', etc., with the modified vacuum Ra
bi frequency g'. These new peaks and the observed shift of the vacuum Rabi
splitting are to be explained in the language of the quasienergy levels ind
uced dynamically by the strong driving held. In the presence of significant
damping the spectrum reflects the photon-number distribution inside the ca
vity, and particularly, a bimodality of the distribution results in a uniqu
e quintuplet resonance fluorescence spectrum.