We study numerically the one-dimensional Kondo and Hund lattices consisting of localized spins interacting antiferro or ferromagnetically with the itinerant electrons, respectively. Using the Density Matrix Renormalization Group we find, for both models and in the small coupling regime, the existence of new magnetic phases where the local spins order forming ferromagnetic islands coupled antiferromagnetically. Furthermore, by increasing the interaction parameter $|J|$ we find that this order evolves toward the ferromagnetic regime through a spiral-like phase with longer characteristic wave lengths. These results shed new light on the zero temperature magnetic phase diagram for these models.
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