“Slates” in the Schiefergebirge east of the Rhine contain tectonically deformed sedimentary dykes. The present orientations of the sand dykes relative to cleavage and bedding allow one to identify discrepancies of more than 30° between the cleavage and the XY-plane of the macroscopically defined finite strain ellipsoid in some localities. Further, microscopic evidence of a non-coaxial strain history is provided by curving fibre “strain shadows”. Individual surfaces composing the anastamosing cleavage are considered to have been generated in or near local principal plane orientations although the mean cleavage plane deviates from the principal plane of the bulk finite strain ellipsoid. This is because the cleavage has been “frozen in” to the rock fabric as material surfaces which could not keep pace with the rotation of the strain axes and is also due to the cleavage-forming processes having been operative only at an advanced stage in the strain history. The spaced, stylolitic nature of the cleavage, as opposed to the penetrative fabric of classic “slaty” cleavages, is attributed to a relatively thin sedimentary cover at the time of cleavage formation.