Are they Firewire drives? If they are USB(2) then they won't be bootable. If they are Firewire drives, is their firmware up-to-date? If not, then that could be a source of your problems. Check the manufacturers site for updates and/or visit
FireWire Depot and click the Firmware Info link at the top of the home page to get an application for determining and installing firmware updates.
If you are using 10.4, try installing the latest update for it to see if it helps. N.B. You can install updates using the standalone combo installers by selecting your external drive as the destination (if it has the OS installed already) rather than your internal boot drive during the installation process. You aren't limited to installing it onto a boot drive.
Edit: Just as a FYI for anyone who stumbles on this thread in the future. For an external to be bootable on your Mac, you may need to update the OS to a version equivalent to or later than the one it shipped with. E.g. My PB shipped with something like OS X 10.3.5 (IIRC) already installed on it - that is, it was released after 10.3 had been out for a while. I installed 10.3.0 onto an external and it would not boot my PowerBook until I had also updated it to 10.3.5.