Precise radial velocity measurements (sigma similar to 20 m s(-1)) of alpha Boo taken over eight consecutive nights in 1992 June are presented. A periodogram of the data shows significant power at periods of 2.46 days and 3.8 days. A separate analysis, using nonlinear least-squares fitting, reveals an additional period at 8.5 days, but at a very low amplitude(similar to 14 m s(-1)), in addition to 2.46 day and 4.03 day periods. However, the 1.84 day period found by Smith et al. is not found in these data. The expected periods of the fundamental and first harmonic modes of radial pulsations were estimated using the radius determination of Di Benedetto and Rabbia, published log g values, and the empirical Q(M, R) relationship of Cox, King and Stellingwerf. The 2.46 day period is near that expected for the fundamental or first harmonic radial mode, depending on the choice of stellar mass which is uncertain due to the wide range of surface gravity determinations. For a given mass and radius the 1.84 day period found by Smith et al. coincides with that of the next harmonic. These periods indicate that the shortterm variability of alpha Boo may be explained by radial pulsations. Furthermore, it seems that this star has switched pulsation modes to a lower overtone from the time of the Smith et al. measurements. A recent investigation into the excitation of acoustic oscillations in alpha Boo by Balmforth, Gough, and Tout reveals peaks in the growth rates of modes having periods very near those observed in alpha Boo for a stellar model of 0.23 M(.). This low value of the mass, however, is inconsistent with stellar evolution theory and a recent determination of the surface gravity of this star. It is clear that alpha Boo is multiperiodic and may be changing modes on timescales of a few years. This star may thus be an ideal candidate for the application of pulsation theory to late-type, evolved stars and may provide important tests of stellar evolution theory.