Elude means evade, or be hard to grasp. "Tom eluded his captors by hiding under a table. Martha tried to understand chemistry, but the subject continued to elude her."
Elude has a slippery feeling to it. You elude the police, math can elude you — and that yak you went to see on safari but never got a glimpse of, you might say that he has eluded you as well. Delude means "to deceive," and there are times when someone can both delude and elude you — like when the conman took your money and then escaped out the back door.