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International audience; This article presents an original work on velocity and stress autocorrelation functions, memory functions, spectral densities and atomic transport properties of two liquid alkali metals (sodium and potassium). For this, we carried out molecular dynamics (MD) simulations using Green-Kubo relation under the condition of very long-time duration to obtain reliable and accurate results.An originality of the present work is that the interatomic forces are described by pair potentials built within the “first principles” pseudopotential formalism using the non-local and energy dependent model potential of Shaw. It is completely free of adjustable parameters since the energy dependent parameters are determined self-consistently at the Fermi energy on an absolute energy scale. The Green-Kubo relationship is the main theoretical tool that allows us determining the atomic transport coefficients from appropriate time-autocorrelation functions. An important new result concerns the memory function. We demonstrate, for the first time to our knowledge, that it can be depicted as a sum of wavelets. The wavelets with their amazing features emphasize the nature of dynamic processes at the microscopic level. We also compared, for the first time to our knowledge, the spectral density associated to the velocity autocorrelation function (VACF), to experimental values obtained by incoherent inelastic neutron scattering. Finally, the temperature dependence of the self-diffusion coefficient (our previous study) and that of shear viscosity (present work) are both in excellent agreement with experiment.