Rat74136's external hard drive is full. He asked the Answer Line forum how to keep backing up.
This is why I have lately come to prefer backup programs like Rebit and Mozy, that automatically remove older versions of files, while keeping only the most recent versions. This keeps the backup down to size and is much simpler.
If your backup doesn't do this, it's best to back up to an external drive large enough to fit two full backup sets (defining a set as one full and several incremental backups), or use two external drives. That way, the only backup you have to delete to make room for a new one is already out of date.
Another option is to make the backup set smaller by removing from it large files that you seldom change, such as photos and music. You can back them up separately, perhaps even burning them to DVD.
As far as your immediate problem is concerned, you have two options. You can buy a second external drive and start a new backup set on that, with the intention of deleting what's on your current drive when that one is full. Or you can take a deep breath and delete everything on the current drive, then immediately start over with a full backup.