Deleting your Hangout message history..
Your Hangout Messages may still be somewhere in the web, and you may be surprised when they suddenly pop up again.
The instructions to delete them are at: support.google.com/hangouts/answer/3112001
After you delete YOUR messages, they will go from all your devices in YOUR account. However, it seems that they will still be available to be seen by the other people in the conversation.
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