  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.
