The cavity field spectra of two atoms interacting with two-mode field with different coupling constant via two-photon resonant transition processes are investigated. The results for the initial fields in coherent state or squeezed vacuum state are presented. The effects of relative coupling constant R=g_2/g_1 and initial field intensity on the spectrum structure are discussed. When the two modes are both in coherent states, the each mode spectrum appears two peeks for small R and three peeks for R≈1. When the two modes are both in squeezed vacuum states, the complicated multi-peak structure appears for weak fields and single classical resonance peak appears for strong field.