1 : half asleep; "made drowsy by the long ride"; "it seemed a pity to disturb the drowsing (or dozing) professor"; "a tired dozy child"; "the nodding (or napping) grandmother in her rocking chair"
2 : ready to fall asleep; "beginning to feel sleepy"; "a sleepy-eyed child with drooping eyelids"; "sleepyheaded students"