One is faced with imminent danger or trouble. In Greek mythology, the courtier Damocles was forced to sit beneath a sword suspended by a single hair to emphasize the instability of a king's fortunes. I know his history of violent behavior, so I feel like a sword of Damocles hangs over my head whenever I'm alone with him.With the threat of nuclear war, many feel that a sword of Damocles hangs over the world's head.