We consider two single-mode semiconductor lasers, which are coupled
face to face via the injection of the optical field. We describe
the symmetries of the coupled rate-equations model, the associated
stationary solutions (synchronous and antisynchronous), and the
bifurcations between them for the case when the propagation delay of the injected field is small. For the coupled lasers with a detuning, we discuss the emergence of self-pulsations with specific properties
(anti-phase, in-phase). We also identify parameter regions, where
chaotic pulsations occur.