Cuprate high-Tc superconductors exhibit enigmatic behavior in the nonsuperconducting state. For carrier concentrations near "optimal doping" (with respect to the highest Tcs) the transport and spectroscopic properties are unlike those of a Landau-Fermi liquid. On the Mott-insulating side of the optimal carrier concentration, which corresponds to underdoping, a pseudogap removes quasi-particle spectral weight from parts of the Fermi surface and causes a breakup of the Fermi surface into disconnected nodal and antinodal sectors. Here, we show that the near-nodal excitations of underdoped cuprates obey Fermi liquid behavior. The lifetime τ(ω, T) of a quasi-particle depends on its energy ω as well as on the temperature T. For a Fermi liquid, 1/τ(ω, T) is expected to collapse on a universal function proportional to (ℏω)(2) + (pπk(B)T)(2). Magneto-transport experiments, which probe the properties in the limit ω = 0, have provided indications for the presence of a T(2) dependence of the dc (ω = 0) resistivity of different cuprate materials. However, Fermi liquid behavior is very much about the energy dependence of the lifetime, and this can only be addressed by spectroscopic techniques. Our optical experiments confirm the aforementioned universal ω- and T dependence of 1/τ(ω, T), with p ∼ 1.5. Our data thus provide a piece of evidence in favor of a Fermi liquid-like scenario of the pseudogap phase of the cuprates.