  We formulate a theory of transport in graphene bilayers in the weak momentum
scattering regime in such a way as to take into account contributions to the
electrical conductivity to leading and next-to-leading order in the scattering
potential. The response of bilayers to an electric field cannot be regarded as
a sum of terms due to individual layers. Rather, interlayer tunneling and
coherence between positive- and negative-energy states give the main
contributions to the conductivity. At low energies, the dominant effect of
scattering on transport comes from scattering within each energy band, yet a
simple picture encapsulating the role of collisions in a set of scattering
times is not applicable. Coherence between positive- and negative-energy states
gives, as in monolayers, a term in the conductivity which depends on the order
of limits. The application of an external gate, which introduces a gap between
positive- and negative-energy states, does not affect transport. Nevertheless
the solution to the kinetic equation in the presence of such a gate is very
revealing for transport in both bilayers and monolayers.
