  We present multiplicity results for the periodic and Neumann-type boundary
value problems associated with coupled Hamiltonian systems. For the periodic
problem, we couple a system having twist condition with another one whose
nonlinearity lies between the gradients of two positive and positively
2-homogeneous Hamiltonain functions. Concerning the Neumann-type problem, we
treat the same system without any twist assumption. We examine the cases of
nonresonance, simple resonance, and double resonance by imposing some kind of
Landesman--Lazer conditions.
