  Given a (smooth) complex analytic family of compact complex manifolds, we
prove that the central fibre must be Moishezon if the other fibres are
Moishezon. Using a "strongly Gauduchon metric" on the central fibre whose
existence was proved in our previous work on limits of projective manifolds, we
show that the irreducible components of the relative Barlet space of divisors
contained in the fibres are proper over the base even under the weaker
assumption that the $\partial\bar\partial$-lemma hold on all the fibres except,
possibly, the central one. This implies that the algebraic dimension of the
central fibre cannot be lower than that of the generic fibre. Since the latter
is already maximal thanks to the Moishezon assumption, the central fibre must
be of maximal algebraic dimension, hence Moishezon.
