Polycrystalline samples RSr2Cu2.7Mo0.307 _ 8 with R = Y, Pr, Gd, and Tb were synthesized and studied by means of powder X-ray diffraction, electrical resistivity, magnetic susceptibility, and specific-heat measurements. All four samples form a perovskite-layer structure with a tetragonal symmetry. The calculated lattice constants using space group P4/mmm indicate that these rare-earth ions are basically in the 3 + valence state. Samples R = Y, Gd, and Tb are superconducting with transitions at around 30 K, while PrSr2Cu2,7Moo.307_~ remains semiconducting down to 2 K. Effective magnetic moments /xon. derived from a Curie-Weiss-behavior susceptibility for R = Gd and Tb are 7.92 /x B and 9.75 /x B, respectively, which are close to those of trivalent free ions. While the /zef f = 3.05 /z B for R = Pr is smaller than that expected for a Pr 3+ free ion. A magnetic ordering transition is observed by a A-type anomaly in specific-heat measurements at 2.27 K and 5.43 K for R = Gd and Tb, respectively. In contrast, no significant feature was observed in specific heat for PrSr2Cu2.vMo0.307-8 in the temperature range 0.6-40 K. The similarities and differences in superconducting and magnetic properties between RSr2Cuz.7Moo.30 7_ ~ and RBa2Cu307_ 8 are discussed.