  This article is concerned with causal structures, which are defined as a
field of tangentially non-degenerate projective hypersurfaces in the
projectivized tangent bundle of a manifold. The local equivalence problem of
causal structures on manifolds of dimension at least four is solved using
Cartan's method of equivalence, leading to an $\{e\}$-structure over some
principal bundle. It is shown that these structures correspond to parabolic
geometries of type $(D_n,P_{1,2})$ and $(B_{n-1},P_{1,2})$, when $n\geq 4$, and
$(D_3,P_{1,2,3})$. The essential local invariants are determined and
interpreted geometrically. Several special classes of causal structures are
considered including those that are a lift of pseudo-conformal structures and
those referred to as causal structures with vanishing Wsf curvature. A
twistorial construction for causal structures with vanishing Wsf curvature is
given.
