  In 1966 Gallai asked whether all longest paths in a connected graph have
nonempty intersection. This is not true in general and various counterexamples
have been found. However, the answer to Gallai's question is positive for
several well-known classes of graphs, as for instance connected outerplanar
graphs, connected split graphs, and 2-trees. A graph is series-parallel if it
does not contain $K_4$ as a minor. Series-parallel graphs are also known as
partial 2-trees, which are arbitrary subgraphs of 2-trees. We present a proof
that every connected series-parallel graph has a vertex that is common to all
of its longest paths. Since 2-trees are maximal series-parallel graphs, and
outerplanar graphs are also series-parallel, our result captures these two
classes in one proof and strengthens them to a larger class of graphs. We also
describe how this vertex can be found in linear time.
