  We study the stability of some strongly frustrated antiferromagnetic spin
lattices in high magnetic fields against lattice distortions. In particular, we
consider a spin-s anisotropic Heisenberg antiferromagnet on the
square-kagom\'{e} and kagom\'{e} lattices. The independent localized magnons
embedded in a ferromagnetic environment, which are the ground state at the
saturation field, imply lattice instabilities for appropriate lattice
distortions fitting to the structure of the localized magnons. We discuss in
detail the scenario of this spin-Peierls instability in high magnetic fields
which essentially depends on the values of the exchange interaction anisotropy
\Delta and spin s.
