An experimental study was conducted to observe the effects of parallel-superposed flow condition on viscoelastic properties of LLDPE, Kevlar fibre reinforced LLDPE and hybrid of short glass fibre and Kevlar fibre reinforced LLDPE. Parallel-plate rheometer was employed for these tests. Rheological parameters such as loss modulus (𝐺″) and dynamic viscosity (𝜂′) do not vary significantly on superposing steady state shear with oscillatory shear in the studied range of experiment at 185°C in un-reinforced LLDPE. Kevlar fibre reinforced LLDPE and Kevlar/glass fibre reinforced LLDPE showed significant changes in the flow behaviour under various sets of superposed conditions. Storage modulus (𝐺′), and 𝐺″ become highly sensitive to low oscillatory angular frequencies (𝜔) under superposed conditions. These curves show two different regions with increased 𝜔 value. At low 𝜔 values, parameters 𝐺′ and 𝐺″ change sharply reaching a certain value, thereafter, changes are moderate with increased 𝜔. In case of 𝜂′ a maxima is observed, position of which, depends upon the value of steady shear rate. Maxima shifts towards higher frequencies with the increased steady shear rate.