The previously unreported RE3Mo14O30 and RE2Mo9O19 phases were synthesized in vacuo from rare-earth oxides, molybdenum oxide, and molybdenum metal using halide fluxes at 875-1000 degrees C. Both phases adopt structures in the triclinic P (1) over bar space group albeit with several notable differences. The structures display an ordering of layers along the a direction of the unit cell, forming distinct honeycomb-related lattice arrangements composed of MoO6 octahedra and vacancies. Mo-Mo bonding and clusters are present; the RE3Mo14O30 structure contains Mo dimers and rhomboid tetramers, while the RE2Mo9O19 structure contains rhomboid tetramers and an unusual arrangement of planar tetramers, pentamers, and hexamers. The magnetic measurements found the RE2Mo9O19 phases to be simple paramagnets, while La3Mo14O30 was observed to order antiferromagnetically at 18 K. Electrical resistivity measurements confirmed all of the samples to behave as nondegenerate semiconductors.