We study the amplitude modulation of ion-acoustic wave (IAW) packets in an unmagnetized electron-ion plasma with two-temperature (cool and hot) electrons in the context of the Tsallis' nonextensive statistics. Using the multiple-scale technique, a nonlinear Schrödinger (NLS) equation is derived, which governs the dynamics of modulated wave packets. It is shown that in nonextensive plasmas, the IAW envelope is always stable for long-wavelength modes (k→0) and unstable for short-wavelengths with k≳1. However, the envelope can be unstable at an intermediate scale of perturbations with 0
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