Unexplained periodic fluctuations in the decay rates of Si-32 and Ra-226 have been reported by groups at Brookhaven National Laboratory (Si-32), and at the Physikalisch-Technische-Bundesandstalt in Germany (Ra-226). We show from an analysis of the raw data in these experiments that the observed fluctuations are strongly correlated in time, not only with each other, but also with the distance betwe