Synchronization due to a weak global coupling with time delay in a semicond
uctor laser array is investigated both in the cw and self-pulsing regimes.
A generalized form of the: Kuramoto phase equations is derived and discusse
d analytically. The time delay is shown to induce in-phase synchronization
in all dynamical regimes. Another form of synchronization is found which le
ads to local extinction of self-pulsing in the array.