  Let $A = \mathbb{F}_p$ or $\mathbb{Z}_p$, and let $R = A[[x_1]][[x_2;
\sigma_2, \delta_2]]\dots[[x_n;\sigma_n,\delta_n]]$, an iterated local skew
power series ring over $A$. Under mild conditions, we show that
(multiplicative) monomial orders exist, and develop the theory of Gr\"obner
bases for $R$. We show that all rank-2 local skew power series rings over
$\mathbb{F}_p$ satisfy polynormality, and give an example of a rank-2 local
skew power series ring over $\mathbb{Z}_p$ which is a unique factorisation
domain in the sense of Chatters-Jordan.
