  In this paper we study discreteness of complex hyperbolic triangle groups of
type $[m,m,0;3,3,2]$, i.e. groups of isometries of the complex hyperbolic plane
generated by three complex reflections of orders $3,3,2$ in complex geodesics
with pairwise distances $m,m,0$. For fixed $m,$ the parameter space of such
groups is of real dimension one. We determine intervals in this parameter space
that correspond to discrete and to non-discrete triangle groups.
