  Using the notion of complete compactness introduced by H. Saar, we define
completely almost periodic functionals on completely contractive Banach
algebras. We show that, if $(M,\Gamma)$ is a Hopf--von Neumann algebra with $M$
injective, then the space of completely almost periodic functionals on $M_\ast$
is a $C^\ast$-subalgebra of $M$.
