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This is a joint work with Marcelo Viana.We formulate a version of the Avila-Viana Invariance Principle for diffeomorphism cocycles that are not necessary dominated(fiber bunched).As an application,we prove that cocycles having some non-zero Lyapunov exponent are generic in a number of situations,including GL(d)-cocycles over expanding maps and Di (M)cocycles over expanding maps.