A pseudo-Newtonian Hill problem based on the Paczyfiski-Wiita pseudo-Newtonian potential that reproduces general relativistic effects is presented and compared with the usual Newtonian Hill problem. Poincare maps, Lyapunov exponents and fractal escape techniques are employed to study bounded and unbounded orbits. In particular we consider the systems composed by Sun, Earth and Moon and composed by the Milky Way, the M2 cluster and a star. We find that some pseudo-Newtonian systems-including the M2 system-are more stable than their Newtonian equivalent. (c) 2006 Elsevier B.V. All rights reserved.35241763398403