HOW DO I UPGRADE AN OLD IMAC USING OSX10.4.11 TO THE LATEST LION OSX?

Assuming it has a Core 2 Duo or better CPU, you purchase a Mac OS X 10.6 DVD(or get it for free if you're a paid MobileMe member), install it, update to 10.6.8, and then get Lion from the Mac App Store, or purchase the Lion USB thumbdrive and install it onto a blank drive or partition.

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See this tip. And please avoid from using ALL UPPERCASE. In internet lingo, it means you are shouting, not to mention makes it is hard to read. I hope that's not what you meant.

If your iMac has a PowerPC processor, you can upgrade to OS 10.5 Leopard, which is the max OS.

If your iMac has an Intel processor, you can upgrade to OS 10.6 Snow Leopard, and possibly OS 10.7 Lion.

 Cheers, Tom 😉