  Exchange-driven growth (EDG) is a process in which pairs of clusters interact
by exchanging single unit with a rate given by a kernel $K(j,k)$. Despite EDG
model's common use in the applied sciences, its rigorous mathematical treatment
is very recent. In this article we study the large time behaviour of EDG
equations. We show two sets of results depending on the properties of the
kernel $(i)$ $K(j,k)=b_{j}a_{k}$ and $(ii)$ $K(j,k)=ja_{k}+b_{j}
+\varepsilon\beta_{j}\alpha_{k}$. For type I kernels, under the detailed
balance assumption, we show that the system admits equilibrium solutions up to
a critical mass $\rho_{s}$ above which there is no equilibrium. We prove that
if the system has an initial mass above $\rho_{s}$ then the solutions converge
to critical equilibrium distribution in a weak sense while strong convergence
can be shown when initial mass is below $\rho_{s}$. For type II kernels, we
make no assumption of detailed balance and equilibrium is obtained via a
contraction property. We provide two separate results depending on the
monotonicity of the kernel or smallness of the total mass. For the first case
we show exponential convergence in the number of clusters norm and for the
second we prove exponential convergence in the total mass norm.
