  We analyse the momentum dependence of static non-uniform susceptibilities of
layered local-moment systems below Curie (Neel) temperature within the
1/S-expansion, the renormalization-group approach, and first order of
1/N-expansion. We argue that the previously known results of the spin-wave
theory and renormalization-group approach for the transverse spin
susceptibility acquire strong corrections already at sufficiently low
temperatures, which appear due to the interaction of the incomping magnon
having momentum q with magnons with momenta k<q. Such corrections can not be
treated in the standard renormalization-group approach, but can be described by
both, 1/S and 1/N expansions. The results of these expansions can be
successfully extrapolated to the magnetic transition temperature T=T_M yielding
the correct weight of static spin fluctuations, determined by the O(3)
symmetry. For the longitudinal susceptibility, the summation of leading terms
of 1/S expansion within the parquet approach allows to fulfill the sumrule for
the weights of transverse and longitudinal fluctuations in a broad temperature
region below T_M outside the critical regime. We also discuss the effect of
longitudinal spin fluctuations on the (sublattice) magnetization of layered
systems.
