The dielectric loss spectra of a series of copolyesters of poly(ethylene terephthalate) and poly(ethylene isophthalate) have been measured as a function of temperature in a broad frequency range (10(-1)-10(9) Hz). By these measurements, the merging of the two relevant relaxations alpha and beta has been studied. The beta processes exhibit a complex temperature dependence, showing a clear Arrhenius dependence at temperatures well below the glass transition temperature, a transition zone where the characteristic relaxation time of this process nearly does not change with temperature, and an Arrhenius behavior with a higher activation energy for temperatures above the glass transition. The analysis of these results indicates that the beta relaxation in these systems presents typical characteristics of a genuine Johari-Goldstein process. This finding has been interpreted as due to the full monomer extension of the molecular motions involved in the beta relaxation in agreement with recent proposals.