The Magellanic Clouds are well known as being very suitable for observing the various stages of stellar evolution. During the last few years, I have been studying the RR Lyrae variable stars in each of the two Clouds. Some first results were reported at IAU Colloquium No. 21 in 1972 (Graham, 1973). Here, I would like to update these results on the basis of more recent data and to comment on some of the characteristics of the field RR Lyrae stars in each system. Periods and light curves are now available for 63 RR Lyrae stars in a 1° x 1.3° field centered on the cluster NGC 1783 in the Large Magellanic Cloud (LMC) and for 62 stars in a 1° x 1.3° field centered on the cluster NGC 121 in the Small Magellanic Cloud (SMC). Both ab and c type variables are represented and, viewed individually, the Cloud RR Lyraes are identical in characteristics to those known in our Galaxy. Studied as groups, however, there are small but significant differences between the RR Lyrae stars in each system. The following four specific features seem to be emerging from the study.