The muon relaxation rate for the Re-substituted HgSr 2 CaCu 2 O 6ϩy and HgBa 2 Ca 2 Cu 3 O 8ϩy superconductors has been measured as a function of temperature. The low-temperature values of fall close to the universal Uemura line T c (), as observed for other layered superconductors; therefore our data show no evidence of a reduced anisotropy, i.e., interlayer metallization, induced by Re. The in-plane penetration depth values obtained for these 1212 and 1223 compounds are found to be significantly different (ϭ1665 Å and ϭ1310 Å, respectively͒. The roles of the inserted CuO 2 planes, the Ba/Sr substitution and the character of the spacing layers are considered to discuss the observed features. ͓S0163-1829͑99͒00634-7͔