In this paper, we reconsider the recent research studies of $($degenerate$)$ $C$-ultradistribution semigroups and $($degenerate$)$ $C$-ultradistribution cosine functions in locally convex spaces. We follow Komatsu's approach to the theory of ultradistributions, introduce a new condition on the sequence $(M_{p})_{p\in {\mathbb N_{0}}}$ of strictly positive real numbers such that $M_{0}=1$, and slightly improve a great number of structural results obtained in some of author's recent papers.