The invention relates to an organic optoelectronic device, such as a display device, which is protected from the surrounding air by a sealed encapsulation which includes thin layers, and to a method for encapsulating the same. Said device has an electroluminescent unit having at least one active area (5) covered with a multi-layer encapsulation structure (201) and an electric connection area adjacent to the active area, the encapsulation structure including n stack(s) (n≧1) comprising an inorganic film F1, . . . , Fn and a photosensitive layer C1, . . . , Cn, including an internal stack F1/C1 in which F1 covers the active area and C1, which is deposited in a liquid phase, is superposed thereon. According to the invention, the layer or each layer C1, Cn is etched and covers the film F1, . . . , Fn by extending around a peripheral edge (5a) of the active area in at least one structured surrounding portion (210, 211, 212) ending beyond the adjacent connection area, and if n>2, the or each layer C2, . . . , Cn surrounds the layer C1, . . . , Cn−1 of the immediately underlying stack, such that the layer or each layer C1, . . . , Cn passivates the film F1, Fn and laterally protects the underlying active area from the developing solutions and solvents used for etching said layer C1, . . . , Cn.