COMMON If something difficult or unpleasant is hanging over your head or is hanging over you, it worries you because it may cause something bad to happen to you. It is unlikely that the Home Office would want to appoint him to the job if an inquiry was hanging over his head. Miss Evans can now get married without this matter hanging over her. Note: This expression may relate to the story of the Sword of Damocles; see explanation at `sword'.