Let $(X_i,F_i)_{i\ge 1}$ be a sequence of martingale differences.Set $S_n=\sum_{i=1}^{n}X_i$ and $[S]_n=\sum_{i=1}^{n}X_i ^2$. We prove two Cramer type moderate deviation expansions for $P(S_n/\sqrt{[S]_n})\ge x$ as $x\to \infty$. Our results partly extend the earlier work of (Jing, Shao and Wang, 2003) for independent random variables.
