Single crystals of a new mutually incommensurate composite crystal with layered structure, ((\mathrm{BiS}){1.11} \mathrm{NbS}{2}) were synthesized and the average substructures were studied by the single crystal (X) ray diffraction method. The commensurate superlattice reflections along mutually incommensurate directions were observed for the BiS subsystem with the main diffractions of the (\mathrm{NbS}{2}) subsystem. The (\mathrm{NbS}{2}) subsystem with (a=5.7504(9) \AA, b_{1}=3.3306(11) \AA), (c=23,0001(17) \AA, Z=4), and space group (F 2 \mathrm{~mm}) takes the form of (2 \mathrm{H})-type (\mathrm{NbS}{2}) sandwiches with (\mathrm{Nb}) atoms trigonal-prismatically coordinated by (S) atoms. The BiS subsystem with (a=5.752(4) \AA), (b{2}=36.156(5) \AA, c=23.001(5) \AA, Z=48), and space group F2mm has distorted two-atom-thick double layers with an (\mathrm{NaCl}-) type superstructure. The superstructure has (\mathrm{Bi}-\mathrm{Bi}) bonds and nonbonded S-S pairs along mutually incommensurate directions. The periodic Jength of (b_{2}) is six times as large as those of simple (\mathrm{NaCl})-type arrangements. The (\mathrm{Bi}-\mathrm{Bi}) bonds are located in each half-length of (b_{2}) in the BiS double layers. Each (\mathrm{NbS}{2}) sandwich and BiS double layer stack alternately to form a mutually incommensurate composite crystal with a layered structure. The structural relations among ((\mathrm{BiX}){x} T X_{2}(T=\mathrm{Nb}, \mathrm{Ta} ; X=\mathrm{S}, \mathrm{Se})) type compounds are also discussed. o 1995 Academic Press, Inc.