The crystal structures of six members of the homologous series with general formula [BiQX]₂[Ag_xBi_1-xQ_2-2xX _2x-1]_N+1 (Q = S, Se; X = Cl, Br; 1/2 ≤ x ≤ 1) and N = 4, 5, or 7 were determined by single-crystal X-ray diffraction. The series are characterized by the parameters N and x and are denoted ^{(N, x)}P. Ag₃Bi₄S₆Cl₃ (x = 0.60) (I), Ag _3.5Bi_3.5S₅Br₄ (x = 0.70) (II) and Ag_3.65Bi_3.35Se_4.70Br_4.30 (x = 0.73) (III) belong to ^{(4, x})P series Ag_5xBi_7-5xQ _12-10xX_10x-3 and adopt the AgBi₆S₉ structure type. The ^{(5, x)}P compound Ag_3.66Bi _4.34S_6.68Br_3.32 (IV), which corresponds to x = 0.61 in Ag_6xBi_8-6xS_14-12xBr_12x-4, crystallizes isostructurally to AgBi₃S₅. The compounds Ag_4.56Bi_5.44Se_8.88Br_3.12 (x = 0.57) (V) and Ag_5.14Bi_4.86S_7.76Br_4.24 (x = 0.64) (VI), which are members of ^{(7, x)}P series Ag _8xBi_10-8xQ_18-16xBr_16x-6, adopt the Ag₃Bi₇S₁₂ structure type. In the monoclinic crystal structures (space group C2/m) two kinds of layered modules alternate along [001]. Modules of type A uniformly consist of paired rods of face-sharing monocapped trigonal prisms around Bi atoms with octahedra around mixed occupied metal positions (M = Ag/Bi) between them. Modules of type B are composed of [MZ₆] octahedra, which are arranged in NaCl-type fragments of thickness N. All structures exhibit Ag/Bi disorder in octahedrally coordinated metal positions as well as Q/X mixed occupation of some anion positions. Corresponding to their black color, all compounds are narrow-gap semiconductors (E_g = 0.35 eV for (II)). General characteristics of the entire class of ^{(N, x)}P compounds are gathered in a catalogue.