Two mass points of equal masses m1 = m2 > 0 move under Newton's law of attraction in a non-collision hyperbolic orbit while their center of mass is at rest. We consider a third mass point, of mass m3 = 0, moving on the straight line L perpendicular to the plane of motion of the first two mass points and passing through their center of mass. Since m3 = 0, the motion of m1 and m2 is not affected by the third, and from the symmetry of the motion it is clear that m3 remains on the line L. The hyperbolic restricted 3-body problem is to describe the moton of m3. Our main result is the characterization of the global flow of this problem. © 1995 Springer-Verlag.