The chalcogenides Ba2Cu4-xSeyTe5-y were synthesized from the elements in stoichiometric ratios at 700 degrees C, followed by annealing at 600 degrees C. The ternary telluride Ba2Cu4-xTe5 crystallizes in a new structure type, space group C2/c, with lattice dimensions of a = 9.4428(6) angstrom, b = 9.3289(6) angstrom, c = 13.3028(8) angstrom, beta = 101.635(1)degrees, V = 1147.8(1) angstrom(3), for x = 0.75(1) (Z = 4). The corresponding selenide-telluride adopts another new, but strongly related, structure type, space group P4(1)2(1)2, with a = 6.5418(3) angstrom, c = 25.782(2) angstrom, V = 1103.3(1) angstrom(3), for Ba2Cu3.26(2)Se0.729(8)Te4.271 (Z=4). Between 0.13 and 1.0 Te per formula unit can be replaced with Se, while the Cu content appears to vary only within 0.67 <= x <= 0.81 for Ba2Cu4-xSeyTe5-y. Despite crystallizing in different crystal systems, the telluride and the selenide-telluride exhibit topologically equivalent structure motifs, namely, chains of Cu(Se,Te)(4) tetrahedra with a Cu atom cis/trans chain as well as an almost linear Te atom chain. All these chalcogenides, as far as measured, are p-doped semiconductors, as determined by Seebeck coefficient and electrical conductivity measurements.