We analyse the locking phenomena arising when an external-cavity diode laser is subjected to optical injection from another uncontrolled diode laser. The system stability is investigated as a function of coupled cavity time delay and the optical injection strength. Different regimes, spanning from 'in-phase locking' to 'out-of-phase locking' with ultimate amplitude death of low-frequency fluctuations/pulsations, are described experimentally as well as numerically for weak to moderate injection. Qualitative agreements between numerically and experimentally observed results for amplitude quenching are shown. Numerical studies describe the shifting of phase-flip bifurcation as the optical injection strength is varied for a particular time delay. Stable phase-locking behaviours, which are desired from the point of view of practical applications, are observed numerically in a wide range of control parameter space. © 2008 IOP Publishing Ltd.