The time-dependent two-photon emission spectra of a two-level atom int
eracting with a single-mode radiation field in an ideal cavity have be
en studied. The expressions of the system operators as a function of t
ime have been derived based on the two-photon Jaynes-Cummings model an
d Heisenberg equation. As a result, the theoretical curves of the time
-dependent two-photon emission spectra have been given. The features o
f two-photon emission spectra depend not only on the photon statistica
l distribution of the initial field, such as the thermal field, the sq
ueezed vacuum field, and the coherent field, but also on the passband
width of the filter detector GAMMA. The two-photon emission spectra ex
hibit multi-peaked structures when GAMMA < lambda (two-photon coupling
constant).