Did you know that folds form in transtension? Obviously they can for transpression, because this is the situation where a shear zone is squeezed so that it gets narrower. Transtension is where simple shear, typically in the form of a vertical shear zone with horizontal layers, is acting together with a simultaneous pure shear that widens the zone (extension perpendicular to the zone) and correspondingly shortening the zone in the vertical direction.
For simple shear, folds nucleate at ca. 45° to the shear zone and rotate toward parallelism with the zone. In transtension, folds form at >45° to the shear zone, and they rotate toward a fixed position (closer to, but still >45°). This fixed position is the orientation of the divergence vector (or flow apophysis if you like). Hence transtension folds always form a high angle to the shear zone.
If the pure shear component is strong, only very open folds form (and the rate of fold amplification is slow), but for simple shear-dominated transtension the folds can get tighter (and amplify faster).
Constrictional strain is a trademark of transtension, and the constriction causes very strong stretching along the fold hinges. This may be manifested by L-tectonices or boudinaged/veined fold hinges (figure on right).
There are several settings and areas where transtensional folds may be found or expected to be found, particularly in areas of oblique rifting (e.g. the Gulf of California), and in areas of (oblique) orogenic collapse (Norwegian Caledonides and perhaps even Death Valley).
If you want to read more about transtensional folding and examples of where it may apply, there is a new Journal of Structural Geology paper out that goes into this subject in more detail:
Fossen, H., Teyssier, C. & Whitney, D.L. 2013: Transtensional folding. Journal of Structural Geology 56, 89-102.