Periodically spaced amplifiers along a transoceanic fiber links provide the phas e_matching condition for four_wave_mixing because of Kerr nonlinearity. Both ana lytic method and numerical method are used to study the cross_phase modulational sideband instability in fiber links with periodical lump amplifiers. In the ana lytic method, the gain of sideband instability is obtained. In the numerical met hod, by use of split_step Fourier transform method, the frequency spectra of out put optical pulses are obtained in normal and anomalous fiber links, and there a re sidebands in the spectrum configuration. By comparison of the results from tw o the methods, they are constant with each other.