We study the orbits of particles (time-like geodesics) around two fixed black holes when the energy is elliptic, i.e. it does not allow the motion to extend to infinity. Most orbits are chaotic, but in many cases there are also ordered motions around stable periodic orbits. The orbits that fall into the first or the second black hole are separated by unstable periodic orbits. These are the satellite periodic orbits around the black holes when they exist. But for certain intervals of parameters there are no satellite orbits around the first or the second black hole. Then the limiting orbits are like arcs of hyperbolae, reaching the curve of zero velocity.