We report on R_c and K band observations of the optical counterpart to GRB 970508 with the Fred Lawrence Whipple Observatory (FLWO) 1.2m telescope. Eleven R_c-band observations were obtained on 1997 May 12, and three on May14. The counterpart clearly faded between the two nights. On May 12 there was no evidence for variability (<9%) on 10-70 minute time scales based on 11 R_c-band observations. On May 19 a one hour observation set a limit on the K magnitude of K>18.2. Comparison of these data points with those obtained by other authors shows that the decay of the optical counterpart can be well fitted by a power law of the form f ~ t**-alpha where alpha = 1.22 +/- 0.03 with occasional fluctuations superposed. We note that the decay of the optical counterpart to another burst, GRB 970228, can also be well fitted with a power law with exponent alpha = 1.0/+0.2/-0.5 with occasional fluctuations superposed. These two decay light curves are remarkably similar in form to that predicted by cosmic-fireball models.
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