  Relaxation theorems for multiple integrals on W^{1,p}(\Omega;\RR^m), where
p\in]1,\infty[, are proved under general conditions on the integrand
L:\MM\to[0,\infty] which is Borel measurable and not necessarily finite. We
involve a localization principle that we previously used to prove a general
lower semicontinuity result. We apply these general results to the relaxation
of nonconvex integrals with exponential-growth.
