We present the derivation of the SO(8) supergravity theory by dimensional reduction of the supergravity theory in 11 dimensions to 4 dimensions. It has been found that the equations of motion are invariant under the global non-compact group E 7(+7) . They can be derived from a family of Lagrangians invariant under a local compact group SU(8). The general procedure to deal with non-compact global internal symmetry without introducing ghosts is discussed in connection with the appearance of an associated compact local symmetry and the use of a non-linear realization of the non-compact group. The supersymmetry transformation rules have been partially derived by dimensional reduction; their complete form follows from the assumption of covariance with respect to E 7 and SU(8). We also present briefly the O( N ) supergravities N = 7, 6, 5 and explain the symmetry SU(4)×SU(1, 1) found for the O(4) supergravity.