Lorentzian extrinsic symmetric spaces Abstract: A non-degenerate submanifold of a pseudo-Euclidean space is called an extrinsic symmetric space if it is invariant under the reflection at each of its normal spaces. Similar to usual symmetric spaces extrinsic symmetric spaces can be characterised by curvature. They are exactly those connected complete submanifolds whose second fundamental form is parallel. We describe extrinsic symmetric spaces by their associated infinitesimal objects. We sketch a structure theory for these algebraic objects. As an application we classify all Lorentzian extrinsic symmetric spaces in arbitrary pseudo-Euclidean spaces.