Based on the chirped soliton solutions of the nonlinear Schr?dinger equation with cubic-quintic variable coefficients under Raman effect, the spectral evolution characteristics of chirped one-soliton and two-soliton in a saturable inhomogeneous fiber system with a periodic dispersion distribution are studied. The results show that in both homogeneous and inhomogeneous fibers, the high order effects do not affect the soliton waveforms in time domain, but directly influence their spectra, because they are only related to the phase of the solitons. In the homogeneous fiber, the chirp parameters of solitons are reduced to zero and the high-order effects make the spectrum of unchirped one-soliton redshift and the accompanied sidelobe appear at the side of high frequency. Compared with the one-soliton, the two-soliton with parallel transmission or colliding evolution shows splitting in its spectrum, and the high-order effects enhance the spectral splitting of two-soliton. Compared with the properties of one-soliton and two-soliton in a homogeneous fiber, the periodical change of chirp parameters in a periodic dispersion-distributed fiber causes that the pulse width and spectrum of one-soliton are periodically compressed and expanded. In contrast, as for the two-soliton, its spectrum is significantly broadened during collision and the chirp makes the spectrum of two-soliton blueshift for two-soliton with quasi-parallel transmission or colliding evolution, while the high-order effects make the spectrum redshift. The presented results are of great significance to study the spectral characteristics of high power signals in ultrafast optical communication systems.