  We show the existence of non-Hermitian degeneracies, known as exceptional
points, in the collective mode spectrum of Fermi liquids with quadrupolar
interactions. Through a careful analysis of the analytic properties of the
dynamic quadrupolar susceptibility, we show that, in the weak attractive
region, two stable collective modes coalesce to an exceptional point. We
completely characterize this singularity, explicitly showing its topological
properties. Experimental signatures are also discussed.
