In this paper, we introduce and check some properties of $H-C-$cosine and mixed $C-$cosine families of bounded linear operators on non-Archimedean Banach spaces. We show some results for $H-C-$cosine and mixed $C-$cosine families of bounded linear operators on non-Archimedean Banach spaces. In contrast with the classical setting, the parameter of a given mixed $C-$cosine family of bounded linear operators belongs to a clopen ball $\Omega_{r}$ of the ground field $\mathbb{K}.$ Examples are given to support our work.