  In this article we consider the existence of a family of doubly-symmetric
periodic orbits in the spatial circular Hill's lunar problem, in which the
secondary primary at the origin is oblate. The existence is shown by applying a
fixed point theorem to the equations with periodical conditions expressed in
Poincare-Delaunay elements for the double symmetries after eliminating the
short periodic effects in the first-order perturbations of the approximated
system.
