The accumulation of line dislocations at a block in a slip-plane is considered. The dislocations are taken to be continuously distributed and their speed is taken to be proportional to the (appropriate component of) stress. The external stress is assumed to be constant. At large times, the speed, the crack extension force a(t) at the block and the dislocation density approach their equilibrium values as \(e^{\nu_ 0t/N}\), where \(\nu_ 0=-0\cdot 8375\) is the zero of \(J_{\nu}(\nu)\) with the greatest real part and N is a measure of the number of dislocations. For an arbitrary, but small, initial departure from an equilibrium pile-up, the increment in the crack extension force a(t) is found to vary at small times as \(t^{1/3}\). Associated approximations are also found for the speed and density at small times. These results are obtained by converting the (integro-differential) transport equation for the density into a first-order partial differential equation that contains the crack extension force a(t) as a forcing term. The factor a(t) is then shown to satisfy an integral equation of convolution type amenable to transforms. The re-equilibrium pile-up after a step jump in the external stress is especially simple and is treated first as a prototype.