  Multi-component integrable generalizations of the Fokas-Lenells equation,
associated with each irreducible Hermitian symmetric space are formulated.
Description of the underlying structures associated to the integrability, such
as the Lax representation and the bi-Hamiltonian formulation of the equations
is provided. Two reductions are considered as well, one of which leads to a
nonlocal integrable model. Examples with Hermitian symmetric spaces of all
classical series of types A.III, BD.I, C.I and D.III are presented in details,
as well as possibilities for further reductions in a general form.
