We consider the effect of the exchange disordering, mainly the nonmagn
etic dilution, on the low-temperature properties of the quasi-one-dime
nsional classical antiferromagnets. Dynamic susceptibility expansion i
n defect concentration shows that even a low level of doping substanti
ally changes the spin-wave stiffness and the transverse susceptibility
. We investigate the nonperturbative concentration dependencies of the
spin-wave velocities and susceptibility arising when the impurity con
centration exceeds the small characteristic value x0 = square-root J(p
erpendicular-to)/J(parallel-to). A general result, pertinent to the tr
ue three-dimensional antiferromagnets as well, concerns the excitation
spectrum of the disordered nonfrustrated antiferromagnets with nonflu
ctuating anisotropy. In this case the hydrodynamical description of lo
ng-wave excitations breaks down, and the spin waves with energies near
the anisotropy gap are overdamped.