In the first part [the authors, Acta Astronaut. 11, 415-422 (1984; Zbl 0551.70004)] we have analyzed three-body systems satisfying the condition \(r\leq kR\), where k is a suitable constant, r the mutual distance of the two masses of the ''binary'' and R the distance between the center of mass of the binary and the ''third mass''. In this second part we look for initial conditions under which the inequality \(r\leq kR\) will remain forever satisfied and we develop the corresponding tests of escape and their applications. This leads to a major improvement of the knowledge of the nature of three-body motions especially in the vicinity of triple close approaches.