  For each integer $k>0$, let $n_k$ and $m_k$ be integers such that $n_k\geq 2,
m_k\geq 2$, and let $\mathcal{D}_k$ be a subset of $\{0,\dots,n_k-1\}\times
\{0,\dots,m_k-1\}$. For each $w=(i,j)\in \mathcal{D}_k$, we define an affine
transformation on~$\R^2$ by $$
  \Phi_w(x)=T_k(x+w), \qquad w\in\mathcal{D}_k, $$ where
$T_k=\operatorname{diag}(n_k^{-1},m_k^{-1})$. The non-empty compact set $$
E=\bigcap\nolimits_{k=1}^{\infty}\bigcup\nolimits_{(w_1w_2\ldots w_k)\in
\prod_{i=1}^k\mathcal{D}_i} \Phi_{w_1}\circ \Phi_{w_2}\circ \ldots\circ
\Phi_{w_k} $$ is called a \textit{self-affine Moran set}.
  In the paper, we provide the lower, packing, box-counting and Assouad
dimensions of the self-affine Moran set $E$. We also explore the dimension
properties of self-affine Moran measure $\mu$ supported on $E$, and we provide
Hausdorff, packing and entropy dimension formulas of $\mu$.
