One says that the Tits alternative holds for a finitely generated group ¡ if ¡ contains either a non abelian free subgroup or a solvable subgroup of finite index. Rosenberger states the conjecture that the Tits alternative holds for generalized tri- angle groups T(k, l,m,R) = ha, b; ak = bl = Rm(a, b) = 1i. In the paper Rosenberger’s conjecture is proved for groups T(2, l, 2,R) with l = 6, 12, 30, 60 and some special groups T(3, 4, 2,R).