  Based on the effective four-band model we analyze the spin response in the
normal and superconducting states of the Fe-pnictide superconductors. While the
normal state spin excitations are dominated by the continuum of the
interorbital antiferromagnetic fluctuations and the intraband spin density wave
fluctuations, the unconventional superconductivity yields different feedback.
The resonance peak in form of the well-defined spin exciton occurs {\it only}
for the interband scattering at the antiferromagnetic momentum ${\bf Q}_{AFM}$
for the $s_\pm$ (extended s-wave) superconducting order parameter and it
disappears rapidly for ${\bf q} < {\bf Q}_{AFM}$. The resonance feature is
extremely weak for the $d_{x^2 -y^2}$-wave order parameter due to specific
Fermi surface topology of these compounds. The essential difference between
$s_\pm$-wave and $d_{x^2 -y^2}$-wave symmetries for the magnetic excitations
can be used for experimental determination of the superconducting wave function
symmetry.
