  Theoretical predictions for Bhabha scattering at the two-loop level require
the inclusion of hadronic vacuum polarization in the photon propagator. We
present predictions for the contributions from reducible amplitudes which are
proportional to the vacuum polarization $\pi(q^2)$ and from irreducible ones
where the vacuum polarization appears in a loop representing vertex or box
diagrams. The second case can be treated by using dispersion relations with a
weight function proportional to the $R$-ratio as measured in electron-positron
annihilation into hadrons and kernels that can be calculated perturbatively. We
present simple analytical forms for the kernels and, using two convenient
parametrizations for the function $R(s)$, numerical results for the quantities
of interest. As a cross check we evaluate the corresponding corrections
resulting from light and heavy lepton loops and we find perfect agreement with
previous calculations. For the hadronic correction our result are in good
agreement with a previous evaluation.
