Progress has been made in understanding the stability of hierarchical three-body systems where the third body moves on an approximately Keplerian orbit about the centre of mass of the binary, at a distance large compared to the binary separation. Harrington (1968,1969) showed analytically that provided the third body was sufficiently distant from the binary no secular terms appeared in the semi-major axis and the system was stable. Harrington (1972,1975,1977) established numerically a critical minimum separation distance (or period) for a stable system in terms of the masses, unaffected by the relative inclinations of the orbits, except for angles close to 90°. Most subsequent investigations have therefore used planar configurations. Graziani & Black (1981), Black (1982) and Pendleton & Black (1983) again using long-term integration of the orbits obtained a criterion for high and low mass binaries. Donnison & Mikulskis (1992,1994,1995) carried out numerical integrations on prograde, retrogade, planetary and stellar triple systems and found for prograde systems very good quantitative agreement with the c
H method. Eggleton & Kieselva (1995) suggested a critical distance ratio approximation determined by the masses in the system. Systems with eccentric orbits are covered using the period ratio determined by Kepler’s third law.