The relaxation of stresses associated to extrinsic grain-boundary dislocations (EGBDs) in singular Sˆ3, {111}, in vicinal Sˆ11, {311} and in general Sˆ11, {332} grain boundaries (GBs) has been investigated by in-situ transmission electron microscopy (TEM) using weak-beam conditions. In a singular Sˆ3, {111} GB, reactions of combination and annihilation occur between extrinsic and intrinsic dislocations when they initially intersect each other. These reactions yield the parallelism of the two types of dislocation which is the preliminary con® guration for any of the existing incorporation models to operate, but further evolution by decomposition of the EGBDs in glissile and sessile components, which can move away, as depicted by theory, was observed once only at a very high temperature. Furthermore, the rearrangement of all the sessile dislocations, extrinsic and intrinsic, in a periodic network was not observed, even after maintaining the thin foil at 9308Cˆ0:6T m (T m is the melting temperature) for a long time. In vicinal Sˆ11, {311} GBs, the continuous spreading of EGBD contrasts, previously observed by TEM in bright-® eld conditions, has been proved to be a decomposition process. Indeed, owing to the weak-beam technique, the wide image of a relaxed EGBD has been resolved in a set of small segments resulting from the interaction between the EGBD and the intrinsic dislocations. After annealing the thin foil at temperatures up to 0.4T m , all the GBDs had rearranged themselves in a quasiperiodic network, indicating that equilibration is almost achieved. In general Sˆ11, {332} GBs, the widening of the EGBD contrasts has never been associated with a decomposition phenomenon. No discrete product of EGBD decomposition has ever been observed by TEM, even in weak-beam conditions. The di erences between the accommodation processes according to the GB type are discussed by referring to the GB atomic structure as described by the structural unit model.