  We consider the classical Yaglom limit theorem for a branching Markov process
$X = (X_t, t \ge 0)$, with non-local branching mechanism in the setting that
the mean semigroup is critical, i.e. its leading eigenvalue is zero. In
particular, we show that there exists a constant $c(f)$ such that \[
  {\rm Law}\left(\frac{\langle f, X_t\rangle}{t} \bigg| \langle 1, X_t\rangle >
0 \right) \to {\mathbf e}_{c(f)}, \qquad t \to \infty, \] where ${\mathbf
e}_{c(f)}$ is an exponential random variable with rate $c(f)$ and the
convergence is in distribution. As part of the proof, we also show that the
probability of survival decays inversely proportionally to time. Although
Yaglom limit theorems have recently been handled in the setting of branching
Brownian motion in a bounded domain and superprocesses, \cite{Ellen, Yanxia},
these results do not allow for non-local branching, which complicates the
analysis. Our approach and the main novelty of this work is based around a
precise result for the scaled asymptotics for the $k$-th martingale moments of
$X$ (rather than the Yaglom limit itself). We then illustrate our results in
the setting of neutron transport, for which the non-locality is essential,
complementing recent developments in this domain \cite{SNTE, SNTEII, SNTEIII,
MCNTE, MultiNTE}.
