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Bistability in a semiconductor ring laser with two external optical injections is studied theoretically, numerically, and experimentally. Two optical injections are added to the two counterpropagating modes in the laser respectively. We first predicted theoretically that, with one of them acting as a static holding beam, the intensities of both modes will form a hysteresis loop as a function of the intensity of the second injection due to nonlinear mode competition. The bistability and the hysteresis characteristics such as its width depend heavily on the intensity of the holding beam. Average switching power will increase as the intensity of the holding beam is increased, accompanied by shrinking width of the hysteresis loop. Numerical simulations and experiment are then carried out to verify the theoretical prediction, and the hysteresis loops at different holding beam strength are plotted. The numerical results together with the qualitative experimental results demonstrate what has been predicted by the theoretical analysis, and a good agreement is obtained. The interaction between the two injections demonstrates potentials for application in all-optical digital signal processing.