1. 睡着的；熟睡的
Someone who is asleep is sleeping.
asleep的意思
e.g. My four year-old daughter was asleep on the sofa.
我4岁的女儿在沙发上睡着了。
2. 入睡；睡着；进入梦乡
When you fall asleep, you start sleeping.
e.g. Sam snuggled down in his pillow and fell asleep.
萨姆舒服地枕着枕头进入了梦乡。
3. 熟睡的；酣睡的
Someone who is fast asleep or sound asleep is sleeping deeply.
e.g. They were both fast asleep in their cots...
他们俩在婴儿床上酣睡着。
e.g. Turning over, she was soon sound asleep again.
她翻了个身，很快又沉沉睡去。