The title compounds were obtained by annealing powders of the alkaline-earth metaperrhenates (M\left(\mathrm{ReO}{4}\right){2} \cdot \mathrm{H}{2} \mathrm{O}) with an excess of the corresponding alkaline-earth halides in open alumina crucibles. The strontium compounds are new. They crystallize with an orthorhombic cell ( (P n m a, Z=4) ). Their structure was determined from single-crystal X-ray data of (\mathrm{Sr}{5}\left(\mathrm{ReO}{5}\right){3} \mathrm{Cl}) : (a=743.80(9) \mathrm{pm}, b=) 1843.4(2) (\mathrm{pm}, c=1056.3(1) \mathrm{pm}, V=1.4483 \mathrm{~nm}^{3}, R=0.02) l for 1850 structure factors and 78 variable parameters. The positions of the heavy atoms correspond to those of the hexagonal apatite structure. This is also the case for the known hexagonal compound (\mathrm{Ba}{5}\left(\mathrm{ReO}{5}\right)_{3} \mathrm{Cl}) whose structure was essentially confirmed by a refinement from single-crystal data: (R=0.024) for 696 F's and 30 variables. The differences and similarities of these structures are discussed considering group-subgroup relationships and near-neighbor environments. Differential scanning calorimetry and high-temperature Simon-Guinier data did not reveal displacive phase transformations of the three strontium compounds to a hexagonal structure up to (650^{\circ} \mathrm{C}). 1993 Academic Press, Inc.