Researchers from UCLA demonstrated an intrinsically stretchable transparent PLED device. The device was fabricated using a simple process that uses single-walled carbon nanotube polymer composite electrodes. The interpenetrating networks of nanotubes and the polymer matrix in the surface layer of the composites lead to low sheet resistance, high transparency, high compliance and low surface roughness.
The new P-OLED prototype can be linearly stretched up to 45% (see photo below) and the composite electrodes can be reversibly stretched by up to 50% with little change in sheet resistance. They say that this is the first stretchable OLED. Back in 2009, researchers from Tokyo demonstrated a stretchable "rubber like" OLED panel which made from many small individual panels (it's not clear whether each small panel was stretchable by itself).