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。