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Summary form only given. Summary from only given. We study theoretically the dynamics of a microchip laser subject to external optical injection and generating the second harmonic (SH) inside its doubly resonant cavity. Two cases of optical injection have been considered and compared; the injection field with a frequency close to the fundamental frequency /spl omega/, of the slave laser and with a frequency close to 2/spl omega/. We show that optical injection opens new potentials for the control of dynamics of a frequency doubling laser. One of such new possibilities is switching the steady states of the slave laser. We have found that in an single-mode frequency-doubling microchip laser subject to optical injection the new relaxation-oscillation to injection of the external optical field. Outside the injection-locking region, we have found the periodic unlocked solutions which become unstable in some regions of the laser parameters and bifurcate to the quasiperiodic solutions. Two bistable branches of the coexisting locked and unlocked states have been analysed.