  We study the low-energy collective excitations and dynamical response
functions of weakly coupled random antiferromagnetic spin-1/2 chains. The
interchain coupling leads to Neel order at low temperatures. We use the
real-space renormalization group technique to tackle the intrachain couplings
and treat the interchain couplings within the Random Phase Approximation (RPA).
We show that the system supports collective spin wave excitations, and
calculate the spin wave velocity and spectra weight within RPA. Comparisons
will be made with inelastic neutron scattering experiments
quasi-one-dimensional disordered spin systems such as doped CuGeO$_3$
