The nature of low-energy excitations in multiwalled nanotubes (MWNTs) is investigated by means of two-color time-resolved photoemission. A careful analysis of the ballistic transport, secondary excitations, and band structure effects was employed in order to extract single electron lifetimes from the observed relaxation trend. It is demonstrated that in the vicinity of the Fermi level the energy dependence of e-e scattering times is inversely proportional to approximately the square of the excitation energy. This result provides strong evidence that electron transport in MWNTs exhibits a Fermi-liquid behavior, indicating that long-range e-e interaction along the tube vanishes due to screening.