expect doing 还是expect to do

都可,但意思上有差别：
表示时间持续的,可以用doing,例：
I expect your coming back.
我（一直）期待着你归来,强调时间上的持续.
而to do,例：
I expect to win the game.
我期望在比赛中获胜,强调对结果的期望.

expect + to do.
look forward to +doing

expect to do...
expect that...

The officer expected his men to do their duty.
The chairman of the committee expect to be back next Thursday.