EPR and electron-nuclear double-resonance (ENDOR) data from F/sup +/ centers in the conduction planes of sodium, potassium and lithium ..beta..-alumina are presented. The low-temperature Ku-band ENDOR spectra from these fast ionic conductors consist of sharp resonances from distant nuclei and broad, unresolved signals from nearest-neighbor aluminum and nearby Na, K, or Li cations in the conduction plane. The Na data are consistent with x-band ENDOR results of others. The K and Li data reveal the existence of a second inequivalent F/sup +/ center in these materials. The shape and breadth of the Na ENDOR signal can be simulated assuming that: (1) both Beevers-Ross and mid-oxygen sites are occupied, (2) the F/sup +/-ligand hyperfine interaction varies with distance as 1/R/sup 3/, and (3) there exists a Gaussian distribution of hyperfine couplings which is consistent with a 0.3-A tunneling distance inferred for Na ions from dielectric susceptibility data on Na ..beta..-alumina.