  We study the non-equilibrium time evolution of the average transverse
magnetisation and end-to-end correlation functions of the random Ising quantum
chain. Starting with fully magnetised states, either in the $x$ or $z$
direction, we compute numerically the average quantities. They show similar
behaviour to the homogeneous chain, that is an algebraic decay in time toward a
stationary state. During the time evolution, the spatial correlations, measured
from one end to the other of the chain, are building up and finally at long
time they reach a size-dependent constant depending on the distance from
criticality. Analytical arguments are given which support the numerical
results.
