  For a finite mean supercriticial Bellman-Harris process, there exist numbers
$\chi_t$ (the Seneta constants) such that $\chi_t$ times the size of the
population at time $t$ converges almost surely to a non-degenerate limit. We
obtain a characterisation of the slowly varying part of the Seneta constants
under the assumption that the life-time distribution of particles is strongly
non-lattice.
