  Landau-Fermi liquid theory is conventionally believed to hold whenever the
interacting single-particle density of states develops a $\delta$-like
component at the Fermi surface, which is associated with quasiparticles. Here
we show that a microscopic justification can be actually achieved under more
general circumstances, even in case coherent quasiparticles are totally missing
and the interacting single-particle density of states vanishes at the chemical
potential as consequence of a pole singularity in the self-energy.
