Let G be an algebraic real reductive group and Z a real spherical G -variety, that is, it admits an open orbit for a minimal parabolic subgroup P . We prove a local structure theorem for Z . In the simplest case where Z is homogeneous, the theorem provides an isomorphism of the open P -orbit with a bundle Q×LS . Here Q is a parabolic subgroup with Levi decomposition L⋉U , and S is a homogeneous space for a quotient D=L/Ln of L , where Ln⊆L is normal, such that D is compact modulo center.