Temperature differences which will exist across the diameters of the Experimental Gas-Cooled Reactor (EGCR) fuel elements will cause the elements to bow. Since the elements are restrained at their midpoints as well as at the ends, the bowing will be accompanied by bending stresses and, as these stresses relax at the relatively high element temperatures, the bowing deflections will increase. A theoretical analysis was developed for predicting the time-dependent bowing behavior of an element subjected to a linearly distributed temperature difference across the diameter. The element behavior was considered to be a combination of creep and elastic bending. The analysis shows that, in every case, the maximum limiting deflection that an element will approach is approximately 2.63 times the initial bowing deflection, or 78% of the maximum deflection the element would have if its midpoint behaved as a plastic hinge. Although the time-dependent bowing will lead to increased temperature gradients, the analysis indicates that the additional deflection produced by the increase will be small compared to the deflection that caused the increase, and, consequently, the elements will be thermally stable.