Misfit layer compounds (MS) nTS 2 (MSn, Pb, Bi, rare earth metals; TNb, Ta, Ti, V, Cr; 1.08 <n< 1.23) are built of alternate double layers of MS, actually a distorted {001} slice of f.c.c. MS (for some compounds hypothetical), and sandwiches of TS 2, with atoms TNb, Ta in slightly distorted trigonal prisms of sulphur atoms (as in the parent compounds 2H-NbS 2 and 2H-NbS 2 and 2H-TaS 2) and atoms TTi, V, Cr in trigonal antiprisms of sulphur atoms ( e.g. as in IT-TiS 2). The MS and TS 2 subsystems have a different geometry in the a- b plane, the stacking direction being c. The MS lattice is approximately quadratic ( a 1≈ b 1 in the range 5.4−6.1 ≅ A ̊ , γ 1 = 90°) while the TS 2 lattice is rectangular ( b 2 a 2 ≈3 1 2 , a 2 in the range 3.3−3.5 Å, γ 2 = 90°). The subsystems are always centred, either C centred ( c ≈ 11−12 Å) or F centred ( c≈22−24 Å). Combinations CC, CF, FC and FF (first MS, second TS 2) were found. Compounds with TNb, Ta have orthorhombic or monoclinic subsystems, the monoclinic angle being β ( β 1 generally not equal to β 2). Compounds with TTi, V, Cr have monoclinic subsystems, the monoclinic angle being α, or triclinic subsystems for which the c axes diverge. Stacking variants ( CC, CF) exist also in this case. Compounds (PbS) 1.14(NbS 2) 2 and (PbS) 1.18(TiS 2) 2 with stacking sequence MSTS 2TS 2MS etc. have been found recently. For all compounds investigated it was found that the subsystems have a common ( b ∗, c ∗ ) reciprocal plane. This stems from the condition that layers cannot intersect and the interaction between M and sulphur of TS 2, the M atoms being in between rows of sulphur of TS 2 parallel to [100]. For the lanthanide (Ln) compounds the distances LnS of the LnS double layer and the distances of Ln to sulphur of TS 2 are about the same and in agreement with Ln(III). The interaction between the subsystems is strong. For MSn, Pb the MS distances of the MS double layer indicate M(II); the interaction between subsystems is weaker than for MLn.