I don't remember Azelf running away but Mesprit you need to go to the lake closest to Twinleaf Town and talk to it and then talk to Professor Oak and get the Poketch app from I think the Poketch company and then have it on your poketch and run. Then you see this face thing and that's Mesprit. It'll "teleport" when you walk too many steps or when you go to a new place. And the damage you get it in battle will be left there. It'll run away so try and have a Pokemon that knows Mean look or something like that.
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Psiycic
Uxie, Mespirit, and Azelf are unavailable in Pokemon SoulSilver. They can, however, be traded from a Diamond, Pearl, or Platinum game, or transferred from a Gen III game.
Dialga, Giratina, Heatran, Mespirit, Uxie, Azelf, Regigigas, Rotom, Cresselia,
on Pokemon yes after you beat the electric gym leader you then can find uxie or mespirit or azelf in the cave
i have been searching for 2 weeks but still no answer so far but you might got mt cornet as may moonstones as pillars put diagla at front with stone and uxie mespirit azelf