  The main purpose of this paper is to investigate degenerate
$C$-(ultra)distribution cosine functions in the setting of barreled
sequentially complete locally convex spaces. In our approach, the infinitesimal
generator of a degenerate $C$-(ultra)distribution cosine function is a
multivalued linear operator and the regularizing operator $C$ is not
necessarily injective. We provide a few important theoretical novelties,
considering also exponential subclasses of degenerate $C$-(ultra)distribution
cosine functions.
