  Thanks to Hubble and Chandra telescopes, some of the large scale jets in
extragalactic radio sources are now being observed at optical and X-ray
frequencies. For the FR I objects the synchrotron nature of this emission is
surely established, although a lot of uncertainties - connected for example
with the particle acceleration processes involved - remain. In this paper we
study production of high energy gamma-rays in FR I kiloparsec-scale jets by
inverse-Compton emission of the synchrotron-emitting electrons. We consider
different origin of seed photons contributing to the inverse-Compton
scattering, including nuclear jet radiation as well as ambient, stellar and
circumstellar emission of the host galaxies. We discuss how future detections
or non-detections of the evaluated gamma-ray fluxes can provide constraints on
the unknown large scale jet parameters, i.e. the magnetic field intensity and
the jet Doppler factor. For the nearby sources Centaurus A and M 87, we find
measurable fluxes of TeV photons resulting from synchrotron self-Compton
process and from comptonisation of the galactic photon fields, respectively. In
the case of Centaurus A, we also find a relatively strong emission component
due to comptonisation of the nuclear blazar photons, which could be easily
observed by GLAST at energy ~10 GeV, providing important test for the
unification of FR I sources with BL Lac objects.
