Summary: This paper establishes asymptotic properties of quasi-maximum likelihood estimators for spatial dynamic panel data with both time and individual fixed effects when the number of individuals $n$ and the number of time periods $T$ can be large. We propose a data transformation approach to eliminate the time effects. When $n / T \rightarrow 0$, the estimators are $\sqrt{nT}$ consistent and asymptotically centered normal; when $n$ is asymptotically proportional to $T$, they are $\sqrt{nT}$ consistent and asymptotically normal, but the limit distribution is not centered around 0; when $n / T \to \infty $, the estimators are consistent with rate $T$ and have a degenerate limit distribution. We also propose a bias correction for our estimators. When $n^{1/3} / T \to 0$, the correction will asymptotically eliminate the bias and yield a centered confidence interval. The estimates from the transformation approach can be consistent when $n$ is a fixed finite number.