The baby was sound asleep (= sleeping deeply) upstairs.
I waited until they were all fast asleep (= sleeping deeply) .
He was so exhausted that he fell asleep at his desk.
She was still half asleep (= not fully awake) when she arrived at work.
The police found him asleep in a garage.
These words all mean to start to sleep.
to start to sleep, sometimes when you do not intend to or in a situation that is not appropriate
When she finally fell asleep, she began to dream.
I pinched myself to stop myself from falling asleep.
to start to sleep, especially when you intend to
I shut my eyes and tried to go to sleep.
He woke for a moment and then went to sleep again.
to start sleeping, especially after a long time or when this is difficult
He took a long time getting to sleep that night.
to fall asleep, especially gradually
I must have drifted off, because when I woke we were nearly home.
( informal ) to fall asleep for a short time, especially when you are sitting down and when you are not supposed to be sleeping
I was practically nodding off in that meeting.
( BrE informal ) to start sleeping lightly
I dropped off and missed the end of the film.