An expansion is developed of the two-point correlation function in the two-time correlation functions up to the expansion terms of third order. This expansion is necessary for the rigorous derivation of kinetic equations that objectively describe physical phenomena in a ‘single’ plasma with Langmuir turbulence. The correspondence of the expansion terms with various physical processes of the traditional weak plasma turbulence theory is discussed. Perspectives are outlined of application of the results to studies in the physics of non-ideal plasmas.