Jump frequencies of Cd tracer atoms were measured in three phases having the orthorhombic Al11R3 structure, with R= La, Ce, or Pr. The structure has four inequivalent Al-sites and two inequivalent R-sites. 111In/Cd tracer atoms were observed to occupy several sites via the nuclear quadrupole interaction using perturbed angular correlation of gamma rays (PAC). Time-domain PAC spectra became damped as the temperature increased, which is attributed to nuclear relaxation caused by diffusional jumps of Cd tracer atoms leading to changes in orientations and/or magnitudes of electric field gradients (EFG’s). Maximum relaxations were observed near 770 K. A method is proposed for estimating the mean jump frequency at that temperature, giving a mean jump frequency w averaged over all sites of about 100 MHz. At still higher temperatures, damping decreased due to motional averaging, and the quadrupole perturbations evolved into unique signals having lower frequencies and corresponding in each phase to the averages of EFG tensors of all sites visited by the Cd tracer atoms. For Al11La3, the jump frequency at 1073 K was estimated to be 1.9 GHz. Such jump frequencies imply unusually high diffusivities in these phases.