We study the existence of stable trajectories, where gas could accumulate to form accretion disks and planets may form, around stars that form binary systems with eccentric orbits.Since the potential is time dependent, no fixed, periodic, close orbits exist. Instead we search for "invariant loops": bundles of orbits that form closed curves in configuration space that change shape in synchrony with the binary orbital phase.Non-intersecting loops can provide the scaffolding for circumstellar and circumbinary disks in these systems.We investigate the range of regions in phase space where these non-intersecting loops can exist and find this to depend on both, the mass ratio of the stars and their orbital eccentricity, with a strong dependence on the latter. The recent discovery ofplanets within close binary systems makes this work very relevant. In fact, we will show a comparison of our theoretical results with the database of binary systems in the solar neighborhood for which orbital parameters are known.