The first two names refer to leaders of the armed wing of the (Christian) Phalangist Party, the Lebanese Forces, and the latter to the militia group itself. Samir Geagea and Elie Hobeika have vied for control of the Lebanese Forces (LF) since March 1985, when Samir Geagea (anti-Syrian) took control of the LF from Fouad Abou Nader, a pro-Syrian leader of the Phalangist militia. [ Henry Degenhardt, ed, Revolutionary and Dissident Movements, (Essex: Longman, 1988), p. 212.] In May 1985, Elie Hobeika was placed in charge of the unit. On 28 December 1985, Hobeika signed an accord with the Syrian government, the Druze militia (PSP), and Amal (pro-Syrian Shi'a militia). The agreement included provisions for the disbandment of Lebanese militia forces and for the initiation of political reforms which would end Christian dominance of Lebanese institutions (parliament, army, etc.). [ Keesing's Record of World Events, Volume XXXII, January 1986, p. 34132.]

Geagea reassumed command of the LF on 15 January 1986, after his anti-Syrian faction, which did not support the December accord, defeated the pro-Syrian faction of Hobeika. Conflict between Hobeika and Geagea continued throughout 1987. In September 1987 a bomb went off near Hobeika's headquarters in Zahle. [ Keesing's, Volume XXXIV, January 1988, p. 35672.] Forces under the command of Geagea reportedly detained scores of people in 1987, many of whom were suspected of being Hobeika supporters. [ Amnesty International Report 1988, p. 246.]
Please see the attached articles:
1) Amnesty International. Amnesty International Report 1988; 1987; 1986. London: Amnesty International Publications.
2) Keesing's Record of World Events, Essex: Longman Group.
Volume XXXII, (January 1986), (August 1986); Volume XXXIII, (March 1987); Volume XXXIV, (January 1988).
3) Henry Degenhardt, ed. Revolutionary and Dissident Movements, Essex: Longman, 1988.