The dispersion relation, instable condition, and the dimensionless critical perturbation frequency and gain spectra of modulation instability(MI) are deduced in metamaterials by directly starting from the extended nonlinear propagation equation including saturable nonlinearity, self-steepening and the second-order nonlinear effects and by adopting the linear stability analy-sis. Variations of the dimensionless gain spectra with the normalized angular frequencies and incident power densities are calculat-ed in the positive refractive-index region of metamaterials. The results show that, in the positive refractive-index region of metamaterials, depending on different normalized angular frequencies and incident power densities, the gain spectra will take on three kinds of forms. Namely, the perturbation frequency is larger than zero, the perturbation frequency is larger than a certain non-ze-ro critical value, and the perturbation frequency is larger than zero but smaller than a certain non-zero critical value. When the normalized angular frequency is small, a certain threshold incident power density is needed for MI to occur. When the incident power density is small, MI can only occur when the perturbation frequency is larger than a certain critical frequency.%直接从异向介质中包含饱和非线性、自陡峭和二阶非线性色散效应的非线性扩展传输方程出发,采用线性稳定性分析法,导出了调制不稳定性的色散关系、不稳定条件、无量纲的临界扰动频率和增益谱.计算和讨论了异向介质正折射区无量纲的增益谱随归一化角频率和入射功率密度的变化关系.结果表明,在异向介质正折射区,随归一化角频率和入射功率密度的不同,增益谱将会出现扰动频率大于零、扰动频率大于某个非零临界值、扰动频率大于零而小于某个非零临界值3种形式.在归一化角频率较小时,调制不稳定性可能出现阈值入射功率密度；且在较小的入射功率密度时,调制不稳定性只能出现在大于某个临界频率时.
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