cease to do　 长时间，甚至永远停做某事。
cease doing　 短时停止做某事，以后还会接着做。

　　That department has ceased to exist forever.
　　那个部门已不复存在。
　　The girls ceased chatting for a moment when their teacher passed by.
　　姑娘们在老师走过时，停了会聊天。