All depends on the amount of ram the new mobo will handle if trying to use all at once. Post the mobo model and we can check,i would say if the ram is compatible with the mobo there should not be any trouble as it should be backward compatible,hence Stuartli's post.
Providing its compatible then yes. But if the DDR400 is running at its full speed then installing the slower DDR333 will slow all the memory down to DDR333 speeds. But it must be compatible ie same parity etc
The motherboard will come with a manual that tells you what speeds of RAM the motherboard supports. The manual is usually also available online (often an updated one) from the manufacturers website.
If you're intending to use mixed memory it may be possible but without knowing the chip numbers of the old and new I don't think anyone can say. Pump the chip numbers into google and you'll get a fuller spec.
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