van Enter A. C. D., Fern\'andez R. Problems with the definition of renormalized Hamiltonians for momentum-space renormalization transformations (48K, LATeX 2e) ABSTRACT. For classical lattice systems with finite (Ising) spins, we show that the implementation of momentum-space renormalization at the level of Hamiltonians runs into the same type of difficulties as found for real-space transformations: Renormalized Hamiltonians are ill-defined in certain regions of the phase diagram.