heoretical 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 contri
butions 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 ve
rtex or box diagrams. The second case can be treated by using dispersion relations with a we
ight function proportional to the $R$-ratio as measured in electron-positron annihilation in
to hadrons and kernels that can be calculated perturbatively. We present simple analytical f
orms for the kernels and, using two convenient parametrizations for the function $R(s)$, num
erical results for the quantities of interest. As a cross check we evaluate the correspondin
g 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.