  In the computation of short-distance cross sections initiated by electrons
and photons one can adopt the so-called structure-function approach, in which
these particles play formally the same roles as hadrons do in QCD factorisation
theorems, and must thus be associated with PDFs (equivalently known as
structure functions in this context). At variance with their QCD counterparts,
such PDFs are entirely calculable in QED. In this paper we present the results,
at the next-to-leading order in the QED coupling constant $\alpha$, for the
initial conditions of the unpolarised electron and photon PDFs, which are a
necessary ingredient for their eventual collinear evolution at the
next-to-leading logarithmic accuracy. We also compute the analogous final-state
quantities, namely the initial conditions for fragmentation functions into
electrons and photons.
