  We study infinite systems of particles which undergo coalescence and
fragmentation, in a manner determined solely by their masses. A pair of
particles having masses $x$ and $y$ coalesces at a given rate $K(x,y)$. A
particle of mass $x$ fragments into a collection of particles of masses
$\theta\_1 x, \theta\_2 x, \ldots$ at rate $F(x) \beta(d\theta)$. We assume
that the kernels $K$ and $F$ satisfy H\"older regularity conditions with
indices $\lambda \in (0,1]$ and $\alpha \in [0, \infty)$ respectively. We show
existence of such infinite particle systems as strong Markov processes taking
values in $\ell\_{\lambda}$, the set of ordered sequences $(m\_i)\_{i \ge 1}$
such that $\sum\_{i \ge 1} m\_i^{\lambda} \textless{} \infty$. We show that
these processes possess the Feller property. This work relies on the use of a
Wasserstein-type distance, which has proved to be particularly well-adapted to
coalescence phenomena.
