In Newtonian mechanics, the two stars move in the conic orbits. The orbits could be bounded, so periodic and stable. They could be unbounded, ie., hyperbolic curves.

In General Relativity, the orbits are nearly conic, as long as the two stars are far away from each other. For example, Mercury orbits around the Sun, and its orbit is not an eclipse but one whose perigee also orbits around the Sun very slowly.

Thank you Shaoqi, I was more questioning about the third objet in my question.

Gabriel

This system is dynamically near the so called restricted three-body problem. There are a few special orbits that can be called stable,

but in general the third body orbits are chaotic and/or unstable.

Mathematically it has been proved that it is IMPOSSIBLE to predict the

motion (for longer than a bit).

Anyway, generally three-body problems (with any masses of the bodies)

is mathematically unsolvable. Meaning that there does not exist

any formula telling the motion. Only numerical computation,

which proceeds in short steps, can tell how the system moves.

For special systems it is sometimes possible to construct

approximate solutions that are practically valid over some longer,

but finite time. Our Solar System is one such many-body system.

See: Article Three-body problem - a deception