PCSX2 is one of the few that is accepted as actually working
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No the Xbox could not run an emulator for the PS2
No, a DS emulator is not compatible with the PS2
Read about the PS2 emulator on the related link
yes a ps2 emulator here is a pretty good one http://www.pcsx2.net
pscx 2 is still the best ps2 emulator out there, and it requires a very strong system cpu/ram/gpu. Emulating a ps2 is a heavy task, so any ps2 emulator will need a high end system. My suggestion is try and find the best GPU pluging.
see both the related links for information on the best working PS2 emulator.
PCSX2 is the only PS2 emulator to consider and they are working on Version 9.9
It allows you to play PS2 games.
The related link allows the download and is a guide to set up a PSCSX2 PS2 emulator
No the emulator does not work with the PS2, it uses the PS2 Bios
http://emulator-zone.com/doc.php/ps2/pcsx2.html - PCSX2 PS2 Emulator.