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We report optical injection-locking in 21-GHz single-section and two-section InAs/InP 1.5-μm quantum-dash mode-locked lasers. Two distinct mode-locked regimes were observed and successfully locked to the optically injected light. The single-section laser only operates as a self-mode-locked laser while the two-section laser could operate as both a self-mode-locked laser and saturable-absorber dominated mode-locked laser. The continuous-wave (CW) injection-locked self-mode-locked laser shows wide tuning of the mode-locked frequency (≈270 MHz) within the locking range. The CW injection-locked saturable-absorber dominated mode-locked laser demonstrates wide optical spectrum, and 5.5 × reduction in the time-bandwidth product of the pulses. Using dual-mode injection, strong reduction of timing jitter ( ≈235 fs) is possible leading to the generation of a wide coherent frequency comb. Coherence between all the modes and the master laser is confirmed by measuring the RF beat note of each mode with a narrow linewidth laser.