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We analyze the stability of phase-locked emission modes of a semiconductor laser subject to both optical feedback and continuous-wave optical injection. We consider a large external cavity and examine the case of weak injection and feedback rates. We find that injection increases the number of excitable resonances in the external cavity and that phase-locked antimodes may bifurcate into a regime of stable bounded phase oscillations. The period of these oscillations is typically on the order of twice the round-trip time.