We present the results of a nonadiabatic, linear stability analysis of models of very low-mass stars (VLMSs) and brown dwarfs (BDs) during the deuterium burning phase in the center. We find unstable fundamental modes with periods varying between ~5 hr for a 0.1 Msun star and ~1 hr for a 0.02 Msun BD. The growth time of the instability decreases with decreasing mass and remains well below the deuterium burning time scale in the mass range considered (0.1--0.02 Msun). These results are robust against variations of the relevant input physics in the evolutionary models. We identify possible candidates for pulsational variability among known VLMSs and BDs in nearby star forming regions whose location in the HR diagram falls within or close to the boundary of the instability strip. Finally, we discuss the possibility that the variability observed in a few objects with periods of ~1 hr can be interpreted in terms of pulsation.
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