We present some recent new developments of the generalized Floquet formulation of time-dependent density functional theory (TDDFT) for nonperturbative treatment of multiphoton processes of many-electron quantum systems in intense monochromatic or multi-color laser fields. It is shown that the periodically or quasi-periodically (polychromatic) time-dependent Kohn-Sham equations can be exactly transformed into an equivalent time-independent Floquet Hamiltonian matrix eigenvalue problems. A procedure is presented for the treatment of bound-bound transitions. For the bound-free transitions, such as multiphoton ionization (MPI) or multiphoton dissociation processes, we introduce the notion of "complex density" and present a non-Hermitian Floquet formalism for the treatment of complex quasienergies of individual spin-orbitals and total many-electron systems. The procedure is demonstrated by a case study of photoionization of He atoms in the photon energy range of 25 to 50 eV. Good agreement with recent experimental data is obtained. We also perform some MPI study of He and Be atoms in intense monochromatic and two-color laser fields.