We present X-ray spectroscopic diagnostics in femto-second laser-driven experiments revealing nonlinear phenomena caused by the strong coupling of the laser radiation with the created plasma. Among those nonlinear phenomena, we found the signatures of the Two Plasmon Decay (TPD) instability in a laser-driven CO₂ cluster-based plasma by analyzing the Langmuir dips in the profile of the O VIII Lyϵ line, caused by the Langmuir waves created at the high laser intensity 3 10¹⁸Wcm^-2. With similar laser intensities, we reveal also the nonlinear phenomenon of the Second Harmonic Generation (SHG) of the laser frequency by analyzing the nonlinear phenomenon of satellites of Lyman δ and ϵ lines of Ar XVII. In the case of relativistic laser-plasma interaction we discovered the Parametric Decay Instability (PDI)-induced ion acoustic turbulence produced simultaneously with Langmuir waves via irradiation of thin Si foils by laser intensities of 10²¹Wcm^-2.