Emission spectra of a pair of effective two-level atoms interacting with two modes of the cavity field through Raman interaction are studied, where the interaction of each atom with the field may be different. The spectra with two modes of the cavity field being initially in various number states are analysed in detail. It is found that emission spectra manifest following new properties: When mode 1 of the cavity field is in vacuum state and the other is in the weak field , the spectrum shows symmetric ten peaks and six peaks alternately, with the increase of R=g2/g1, which reflects the different Raman interacting intensities of two atoms with the cavity field more sensitively compared with the spectrum of two atoms in a single-mode cavity. The spectrum with 01=1, n2=50 and n1 = 50, n2=1 reflects the different positions of mode 1 and mode 2 of cavity field interacting with two atoms through Raman process. Finally, the symmetric 16-peaks structure of the spectrum is explained.