  The paper is dedicated to a system of matrix nonlinear evolution equations
related to a Hermitian symmetric space of the type $\mathbf{A.III}$. The system
under consideration extends the $1+1$ dimensional Heisenberg ferromagnet
equation in the sense that its Lax pair has a form rather similar to the pair
of the original Heisenberg ferromagnet model. We shall present here certain
local and nonlocal reductions. A local integrable deformation and some of its
reductions will be discussed too.
