The estimations of the stability region of the lattice ferromagnetic ground state in the space of model parameters are found. For the triangular lattice strip formed by L segments with the total number of electrons N = L + 1 we derived the effective Hamiltonians describing the low-energy states of the strips and obtained the analytical estimations for above stability region. The possibility of the magnetic transition with the jump of the ground-state spin between minimal and maximal values has also been shown. For the strip with N = L and an alternating value of the one-site potential energy, we have obtained the exact relation between electron parameters, which provides the ferromagnetic character of the lattice ground state. (C) 2001 John Wiley & Sons, Inc.