Steady state solutions to three types of diffusion problems: creep, grain boundary sliding and intergranular crack growth, have been published in the literature. This paper considers, in detail, the events which occur between the time when the external stress is applied and the time when the steady state is eventually reached. The time constant of the transient has been calculated. It is shown how the grain boundary tractions change with time from the initial “elastic” configuration (when sliding has been elastically accommodated) to the steady state “diffusional” configuration (when the sliding rate is diffusionally accommodated). This requires infusion of excess grain boundary dislocations; the distribution of these dislocations is calculated. The results are applied to problems of diffusional creep, grain boundary sliding and intergranular crack growth.