The viscoelastic properties of melts of nanocomposites with partially exfoliated structures, which were composed of low-density polyethylene (LDPE) , ethylene vinyl acetate copolymer (EVA), and montmorillonite and modified by cetyltrimethyl ammonium bromide and octadecyltrimethyl ammonium bromide, were studied. The results obtained through measurements of the dynamic storage modulus G′, the dynamic loss modulus G″, and the transient stress relaxation modulus G(t) of the composites, reveal that the viscoelastic properties of the composites strongly depend on the amount of montmorillonite that is exfoliated into the composites. With the increase in montmorillonite content, the composites show an obvious property of pseudo solid-like materials within the region of lower frequencies (ω). The montmorillonite layers are aligned along the stress direction, and the dependence of dynamic modulus on ω, appears quite different for the composites before and after being exposed to a large amplitude oscillatory shears.