  The magnetic susceptibility of systems from a class of integrable models for
doped spin-$S$ Heisenberg chains is calculated in the limit of vanishing
magnetic field. For small concentrations $x_h$ of the mobile spin-$(S-1/2)$
charge carriers we find an explicit expression for the contribution of the
gapless mode associated to the magnetic degrees of freedom of these holes to
the susceptibility which exhibits a singularity for $x_h\to0$ for sufficiently
large $S$. We prove a sum rule for the contributions of the two gapless
magnetic modes in the system to the susceptibility which holds for arbitrary
hole concentration. This sum rule complements the one for the low temperature
specific heat which has been obtained previously.
