  In this article we study the long time behavior of linear functionals of
branching diffusion processesas well as the time reversal of the spinal process
by means of spectral properties of the Feynman-Kacsemigroup. We generalize for
this non Markovian semigroup the theory of quasi-stationary
distribution(q.s.d.) and Q-process. The most amazing result is the
identification of the law of the reversal time spinalprocess issued from q.s.d.
with the Q-process of the Feynman-Kac semigroup.
