We have determined the ESR properties of UBe13 doped with dilute local moments of Er, Dy, or Gd over the temperature region where there is a large variation in the enhanced specific heat. We find that neither the enhancement, the temperature variation, nor any other anomalous behavior appears to be mirrored in the ESR data. We suggest that this unexpected result must be incorporated into current models of heavy-fermion systems. © 1985 The American Physical Society.552427192722