We study the mod p homology of the double and the triple loop spaces of exc
eptional Lie groups E-6, E-7, and E-8 through the Eilenberg-Moore spectral
sequence and the Serre spectral sequence using homology operations. The Boc
kstein actions on them are also determined. As a result, the Eilenberg-Moor
e spectral sequences of the path loop fibrations converging to H-*(Omega (2
)G; F-p) and H-*(Omega (3) C; F-p) collapse at the E-2-term for any compact
simple Lie group G.