A generalised triangle group has a presentation of the form where R is a cyclically reduced word involving both x and y. When R=xy, these classical triangle groups have representations as discrete groups of isometries of S 2 , R 2 , H 2 depending on In this paper, for other words R, faithful discrete representations of these groups in Isom + H 3 = PSL(2,C) are considered with particular emphasis on the case /? = [x, y] and also on the relationship between the Euler characteristic x and finite covolume representations.1991 Mathematics subject classification: 20H15.