Wendy - I have three external dives connected via USB. They are all "plug-n-play". I can't see what the problem could be if the drives themselves are OK. Two things I can suggest off-hand. First, shut down the computer and unplug both devices. Restart the computer and when up booted up, insert one drive in one USB slot. If that installs, as your original text says it does, then remove this drive and insert the other in the same USB port. If that installs OK then your disks are probably both OK. Now repeat the exercise with the other USB slot. That should test whether the USB port is at fault. If both ports and both drives are OK, then the fault probably lies in the computer's OS confusing two addresses (thinks they're the same). Thus, second thing to try is to restore to earlier settings and try and re-install each drive in turn. (Windows often updates without you knowing it and if you don't fully reboot you can get this sort of problem.)
If these ideas don't work, I would have to know a great deal more about your system to track down hat is happeing, and in that case your best bet is to go the great god GOOGLE and see if a forum therein can help.