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We investigate collective Thomson scattering (CTS) in two-stream non-equilibrium plasmas analytically, numerically and experimentally. In laboratory astrophysics, CTS is a unique tool to obtain local plasma diagnostics. While the standard CTS theory assumes plasmas to be linear, stationary, isotropic and equilibrium, it is often nonlinear, non-stationary, anisotropic, and non-equilibrium in high energy phenomena relevant to laboratory astrophysics. We theoretically calculate and numerically simulate the CTS spectra in two-stream plasmas as a typical example of non-equilibrium system in space and astrophysical plasmas. The simulation results show the feasibility to diagnose two-stream instability directly via CTS measurements. In order to confirm the non-equilibrium CTS analysis, we have been developing experimental system with high repetition rate table top laser for laboratory astrophysics.