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The paper contains the description of the dynamics of non-equilibriumprocesses of spin $s=1$ magnets in an external variable field. We have obtainednonlinear dynamic equations with sources and calculated low-frequencyasymptotics of two-time Green's functions for ferro- and quadrupole magneticstates with $SO(3)$ and $SU(3)$ exchange symmetry of the Hamiltonian. It hasbeen shown that for ferro- and quadrupole magnetic states singularities ofGreen's functions in wave vectors $1/k$, $1/k^2$ and frequencies $1/\omega,1/\omega^2$ have well-known character. We set the exact form of the magneticanisotropy of these Green's functions. For states with $SO(3)$ symmetry of theexchange Hamiltonian, we have found Green's functions with quadrupole degreesof freedom and compared them with Green's functions of magnets having exchange$SU(3)$ symmetry.

Exchange symmetry and low-frequency asymptotics of Green's functions in spin s=1 magnets