  We prove that the crossed product Banach algebra $\ell^1(A,G,\alpha)$ that is
associated with a $\mathrm{C}^\ast$-dynamical system $(A,G,\alpha)$ is amenable
if $G$ is a discrete amenable group and $A$ is a commutative or finite
dimensional $\mathrm{C}^\ast$-algebra. Perspectives for further developments
are indicated.
