Electrolytic oxidation of BEDT-TTF (bis(ethylenedithio)tetrathiafulvalene) in the presence of anionic rhenium thiocyanato complexes has led to the crystallization of two phases containing Re-2(NCS)(10)(n-) (n = 2, 3), while Re(NCS)(6)(2-) and Re-2(NCS)(8)(2-) gave no characterizable products. (BEDT-TTF)(3)[Re-2(NCS)(10)]. 2CH(2)Cl(2) (1) and (BEDT-TTF)(2)[Re-2(NCS)(10)]. C6H5CN (2) are both triclinic () with unit cell parameters a = 12.185(3) Angstrom, b = 13.251(3) Angstrom, c = 14.772(2) Angstrom, alpha = 63.69(1)degrees, beta = 86.56(2)degrees, gamma = 64.50(2)degrees (Z = 1) and a = 13.730(4) Angstrom, b = 14.882(4) Angstrom, c - 16.588(4) Angstrom, alpha - 75.98(2)degrees, gamma = 66.95(2)degrees (Z = 2), respectively. Both salts present packing arrangements of BEDT-TTF not found before. In compound 1 mixed layers of anions and cations contain no stacks of BEDT-TTF. In 2 there are layers of segregated anions and cations, the latter having their long axes nearly parallel to the layers. This compound is the first in which Re-2(NCS)(10)(2-) has been structurally characterized. In both compounds there are numerous close S-S contacts between the NCS ligands and the BEDT-TTF. The compounds are semiconductors, the conductivity being attributed to low-dimensional hopping rather than coherent transport. The magnetic properties of 1 are modeled by a superposition of a Curie-Weiss contribution for the anion and a dimer contribution from the cation.