lt is shown how two fluid dynamical equations for superfluid He' are derived from quantum hydrodynamical Hamiltonian, represented in terms of the quantized canonical con jugate variables, mass density p(x) and velocity field v(x). An essential assumption is that expectation value of v(x) should be identified with the superfluid velocity. The random phase approximation is applied to higher order dynamical correlation function of p and v appearing in the equations of motion. This approximation implies to decouple the correlation into the hydrodynamical degrees of freedom and the incoherent one of thermal phonon. It is found that a set of equations thus obtained is consistent with the two fluid dynamical one, having been widely used in the phenomenological theories. § I. Introduction Two fluid theory for superfluid helium has considerably succeeded in describing the thermodynamical and hydrodynamical phenomena at finite temperature. Nor mal component of fluid at low temperatures can well be described in terms of phonon gas interacting weakly. The two fluid hydrodynamical equations involve various kinetic coefficients which characterize the irreversible processes in phonon gas excited thermally. Therefore, in order to treat the relaxation process of pho non gas and to describe the dynamical behavior of two fluid, it is more fundamental to start with the kinetic stage. This situation is entirely analogous to that encoun tered in the classical normal fluid, apart from the existence of superfluid flow. Landau and Khalatnikov1'· 2' introduced phenomenologically the kinetic equation for phonon distribution function n (p. x) under the existence of superfluid flow. Thus conservation law for mass density p(x), equation of motion for superfluid velocity V 8 (x) and kinetic equation for n (p, x) constitute the basic set of two fluid dynamical equations. 2> The linearized and Fourier transformed expressions of these equations are written as