The spectral behavior of polychromatic spatially fully coherent light diffracted by an annular aperture in the far field is studied. It is shown that the spectrum in the far field is generally different from that at the aperture, i.e., the spectrum in the far field is proportional to the spectrum at the aperture and a spectral modifier, which depends on the central obstruction ratio ε and diffraction angle θ. Detailed numerical calculation results indicate that significant spectral changes take place in the vicinity of zeros of the Airy pattern. It is found that at the critical diffraction angle θc, the spectrum is split into two lines, while at a diffraction angle a little smaller than θc, the spectrum is red-shifted, and at a diffraction angle a little larger than θc, the spectrum is blue-shifted. The influence of the central obstruction ratio on the spectral anomalies is presented.