  The class of 2-interval graphs has been introduced for modelling scheduling
and allocation problems, and more recently for specific bioinformatic problems.
Some of those applications imply restrictions on the 2-interval graphs, and
justify the introduction of a hierarchy of subclasses of 2-interval graphs that
generalize line graphs: balanced 2-interval graphs, unit 2-interval graphs, and
(x,x)-interval graphs. We provide instances that show that all the inclusions
are strict. We extend the NP-completeness proof of recognizing 2-interval
graphs to the recognition of balanced 2-interval graphs. Finally we give hints
on the complexity of unit 2-interval graphs recognition, by studying
relationships with other graph classes: proper circular-arc, quasi-line graphs,
K_{1,5}-free graphs, ...
