IPA: /ˈstɜːrtərəsli/
KK: /stɜrˈtɔrəsli/
In a way that involves loud, heavy breathing, similar to snoring.
He breathed stertorously after running up the hill.
Stertorously is derived from "stertor" (from Latin "stertor", meaning snoring or heavy breathing) and the suffix "-ously" (meaning characterized by). The word describes a manner characterized by snoring or heavy breathing, often associated with sleep or respiratory distress.
Think of the word 'stertor' which relates to snoring or heavy breathing, and remember that 'stertorously' means characterized by that kind of sound.