Receiving a flood of emails from "Postmaster" is bad news. It means that your email address has been harvested by hackers. These hackers use your email address as the "reply to" and send out spam, bulk emails and junk email. When the email address they send to has been discontinued, the postmaster sends an automated message to the "reply to" address--yours. That is why you are getting emails from the postmaster. Take steps to both stop the emails and prevent hackers from using your email address again.
Mark all emails from the postmaster as spam. This will help your email program to recognize these emails as spam and deposit them directly into your spam folder. Delete your spam folder to free up space.
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Retire the email address that is receiving postmaster emails--at least temporarily.
Give yourself more than one email address. Use one for personal email, one for business email, and others for other uses you may think of. This is a small protection; if one of these addresses starts getting postmaster emails, it affects less of your email lists.
Purchase a firewall or other security for your computer. A good security software system will prevent spammers from accessing your email and address lists. Brands widely available include Norton, McAfee, Symantec and Panda.
Beware free downloads. Purchase a reputable security program from a company that has unbiased reviews from multiple sources.