What Celeron processor?

I run a P6BX-A+ motherboard (BX440)with a 333mhz Celeron CPU and want to upgrade. What is the fastest Celeron processor compatible with my motherboard and how easy will the upgrade be?

You wouldn't be doing yourself a big favor by switching to another Celeron in your mobo's range. I doubt the performance would even double.
Your best bet is looking at the newest Cellys and a new mobo (sorry but for what you'd have, it just wouldn't be worth upgrading in same range) if you would like Celerons. An even cheaper way is Durons, and a nice extremly cheap ECS board. It would not even cost you 120$ total, and you can transfer your current RAM (unless PC100) to it. It's up to you and your money, but take my suggestion, because any Celeron below 700 MHZ is just not worth upgrading to, especially when the new ones have 256K L2 and a few nice improvements, plus 0.13m for less heat.

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For the first time, Hookers are hooked on Phonics!!

According to Tekram, this motherboard has a VRM 8.4 Voltage Resistor Module built in. That spec allows for all Coppermine CPU's. The ECS page seems to note a difference between the earlier boards and the 1.1aa/1.2 boards, so those are probably the only ones that have this VRM. The board also supports bus speeds of 133MHz. That means the BEST CPU for it is the PIII 1000EB, as long as you have a newer revision as mentioned. But if you really insist on a Celeron, the 1000 w/128k cache (which is the Coppermine version) should work as well.
Any 133MHz FSB processor would require PC133 memory and a decent graphics card to allow the 133FSB setting.

What's the frequency, Kenneth?

I'd just pop in a faster CPU.

What's the frequency, Kenneth?