  A branching L\'evy process can be seen as the continuous-time version of a
branching random walk. It describes a particle system on the real line in which
particles move and reproduce independently in a Poissonian manner. Just as for
L\'evy processes, the law of a branching L\'evy process is determined by its
characteristic triplet $(\sigma^2,a,\Lambda)$, where the branching L\'evy
measure $\Lambda$ describes the intensity of the Poisson point process of
births and jumps. We establish a version of Biggins' theorem in this framework,
that is we provide necessary and sufficient conditions in terms of the
characteristic triplet $(\sigma^2,a,\Lambda)$ for additive martingales to have
a non-degenerate limit.
