  Consider a critical Erd\"os-R\'enyi random graph: $n$ is the number of
vertices, each one of the $\binom{n}{2}$ possible edges is kept in the graph
independently from the others with probability $n^{-1}+\lambda n^{-4/3}$,
$\lambda$ being a fixed real number. When $n$ goes to infinity, Addario-Berry,
Broutin and Goldschmidt have shown that the collection of connected components,
viewed as suitably normalized measured compact metric spaces, converges in
distribution to a continuous limit $\mathcal{G}_\lambda$ made of random real
graphs. In this paper, we consider notably the dynamical percolation on
critical Erd\"os-R\'enyi random graphs. To each pair of vertices is attached a
Poisson process of intensity $n^{-1/3}$, and every time it rings, one resamples
the corresponding edge. Under this process, the collection of connected
components undergoes coalescence and fragmentation. We prove that this process
converges in distribution, as $n$ goes to infinity, towards a
fragmentation-coalescence process on the continuous limit
$\mathcal{G}_\lambda$. We also prove convergence of discrete coalescence and
fragmentation processes and provide Feller-type properties associated to
fragmentation and coalescence.
