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We investigate the stability domains of ground states of generalized Hubbardmodels with next-nearest neighbour interaction using the optimum groundstateapproach. We focus on the $\eta$-pairing state with momentum P=0 and the fullypolarized ferromagnetic state at half-filling. For these states exact lowerbounds for the regions of stability are obtained in the form of inequalitiesbetween the interaction parameters. For the model with only nearest neighbourinteraction we show that the bounds for the stability regions can be improvedby considering larger clusters. Additional next-nearest neighbour interactionscan lead to larger or smaller stability regions depending on the parametervalues.Comment: 18 pages with 6 figures, LateX2e with BibteX, accepted for  publication in Eur. Phys. J.

Optimum ground states of generalized Hubbard models with next-nearest neighbour interaction