Polylactide (PLA)/organoclay composites were prepared by melt compounding with 4 phr of two different types of organoclays (cloisite 20A and cloisite 30B). Structure development and nonisothermal kinetic of cold crystallization of PLA/organoclay nanocomposites were examined by using of X‐ray diffraction technique, transmission electron microscopy, melt viscoelastic measurements, and differential scanning calorimetry. XRD results demonstrated that the melt intercalation of PLA chains into the cloisite 30B and cloisite 20A galleries was achieved to the same extent. However, it was shown that, PLA/cloisite 20A sample exhibited a significant viscosity upturn and a pronounced nonterminal low frequency storage modulus whose values were greater than those of PLA/cloisite 30B nanocomposite. A detailed analysis of the linear melt viscoelastic properties for the filled and unfilled samples at low frequencies was conducted by fitting the complex viscosity and storage modulus data with Carreau–Yasuda and Fractional Zener models, respectively. The glass transition, cold crystallization, melting temperature, and degree of crystallinity of virgin PLA and PLA/organoclay nanocomposites were inspected. Subsequently, the cold crystallization kinetics was analyzed by Avrami, Jezioney, and Lauritzen–Hoffman kinetic models. It was shown that, the crystallization rate followed Avrami equation with the exponent n around 2.4. From Lauritzen–Hoffman equation and Kissinger model, the nucleation parameter Kg and activation energy were estimated, respectively. J. VINYL ADDIT. TECHNOL., 25:48–58, 2019. © 2018 Society of Plastics Engineers