When a tangent vector X on a Riemaniann manifold satisfies R(X,Y)Z = 0 for all Y,Z, then it is in the kernel of R. The nullity of R is then the dimension of the kernel of R. We examine the case where nullity is n-2, which can be thought of as "almost flat" since symmetry of R rules out a nullity of n-1. These conullity 2 manifolds come up while looking at semi-symmetric spaces. We will end with the result where, if the manifold also has finite volume, then we get a splitting as a surface cross Euclidean space.