Abstract A kinetic equation for the one-particle distribution function has been obtained taking into consideration the spatial density correlation and velocity correlation. To complete the equation in question we have employed the Smolukhovsky generalized equations, which we derived for binary density and binary particle flow. The visco-elastic properties of simple liquids have been investigated in a wide frequency range. The asymptotic behaviour of the viscosity coefficients and their corresponding elasticity moduli, both at low and high frequencies, have been examined. Numerical calculations of analytical expressions for viscosity dynamic coefficients and elasticity moduli are compared with available data in the literature.