It is well known that a cubic del Pezzo surface can degenerate into a cone over an elliptic
curve in a non-singular family. We investigate when a del Pezzo surface (of any degree) can
degenerate into a non-rational surface in a “reasonably good” family. By this we mean a
del Pezzo fibration over a curve in the sense of the Minimal Model Program. We will show
that such degenerations depend on the singularities of the total space of the fibration, and
that there is a correspondence between certain degenerations and del Pezzo fibrations with
an action of a cyclic group.