Series-parallel graphs, which are built by repeatedly applying

series or parallel composition operations to paths, play an

important role in computer science as they model the flow of

information in many types of programs. For directed series-parallel

graphs, we study the problem of finding a shortest path between two

given vertices. Our main result is that we can find such a path in

logarithmic space, which shows that the distance problem for

series-parallel graphs is L-complete. Previously, it was known

that one can compute some path in logarithmic space; but for

other graph types, like undirected graphs or tournament graphs,

constructing some path between given vertices is possible in

logarithmic space while constructing a shortest path is

NL-complete.