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We introduce a spectrum of transpressional and transtensional deformations that potentially result from oblique plate interaction. Five separate types of deformation are designated, in which a simple shear deformation is combined with an orthogonal coaxial deformation. The types vary in the amount of extension v. contraction, both parallel to the margin and vertically. The interaction between the angle of convergence, kinematic vorticity, infinitesimal strain axes, finite strain, and rotation of material lines and planes is investigated. Quantification of the finite strain indicates that the orientation, magnitude, and geometry (flattening, constriction, etc.) change continually during steady-state transpression.These results are then applied to the cases of transpression, particularly resulting from oblique plate convergence of terranes. The obliquity of plate motion and the geometry of the plate margin determine which of the types of transpression or transtension is favoured. A component of margin-parallel stretching also potentially causes terrane motion to locally exceed oblique plate motion, or move opposite to the general direction of movement between the converging plate boundaries. The kinematic models also suggest that the boundaries between converging terranes are likely to exhibit vertical foliation, but either vertical or horizontal lineation. Finally, narrow transpressional zones between colliding blocks may have very high uplift rates, resulting in exhumation of high-grade metamorphic fabrics.