Abstract
It is proven that the lowest excitations Elow(k) of one-dimensional half-integer spin generalized Heisenberg models and half-filled extended Hubbard models are π-periodic functions. For Hubbard models at fractional fillings Elow(k + 2kf) = Elow(k), where 2kf = πn, and n is the number of electrons per unit cell. Moreover, if one of the ground states of the system is magnetic in the thermodynamic limit, then Elow(k) = 0 for any k, so the spectrum is gapless at any wave vector. The last statement is true for any integer or half-integer value of the spin.