The far-zone spectrum of partially coherent light transmitted from a stratified medium is studied. The changes of the far-zone spectrum in the axial and peaxial points are analyzed in detail for the case of a Gaussian Schell-model beam transmitted from a nondispersive slab and a dispersive slab respectively.It is found that the transmitted spectrum may change in many different ways, such as red shifts, blue shifts,line narrowing and splitting into multiple lines. The effective.bandwidth of the incident light and the dispersion of the transmitted medium have a strong influence on the transmitted spectrum in the far zone.