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It is known that there exist two solutions for the He-Ne laser phase locked by synchronous internal phase modulation. One corresponds to a phase difference between adjacent modes of even integers of π (even state) and the other to odd integers of π (odd state). Although their frequency power spectra in general look similar, they appear in the time response as two different sets of pulse trains 180° out of phase with respect to each other. Of the two, for a given set of conditions, it has not yet been possible to predict which state will oscillate. In our observations we find that, if the modulation frequency is fixed slightly higher than the average axial-mode spacing near the line center, the two states can be controlled by varying the amplitude of the modulation signal, resulting in a switching action between the two states. Furthermore, we find that in a narrow region of "detuning" and in a small range of modulation amplitudes, both states oscillate simultaneously. The above results were analyzed by considering the asymmetry in the frequency characteristics of the gain medium due to the presence of the isotope Ne22in the He-Ne mixture. Based on this fact and the concept of "supermode" competition, we give a physical explanation for the observed behaviors. This is supported by the absence of amplitude-dependent switching in a He-Ne tube containing only pure isotope Ne20. We observe also in a He-Ne tube containing 75% Ne20and 25% Ne22the dominance of one state over the other; this result is consistent with the qualitative theory given.