We present the results of a neutron reflectometry study of the kinetics of penetration of a grafted polymer layer into a permanently cross-linked, chemically identical network. The polymer used was polystyrene. Initially the grafted chains are completely excluded from the network, and the interface between them is sharp. The segment density profile was measured after a series of annealing times to follow the kinetics of penetration. The range of annealing times was extended over 9 orders of magnitude by using time-temperature superposition. We observe a slow approach to equilibrium, in good agreement with theory, which predicts this to be logarithmic in time. The kinetics of penetration is slower for more densely cross-linked networks and for greater brush grafting densities. We also note a grafting density dependence of the equilibrium profile but, somewhat unexpectedly, no dependence on the density of cross-links.