We consider the one-orbital N -site repulsive Hubbard model on two kagome like chains, both of which yield a completely dispersionless (flat) one-electron band. Using exact many-electron ground states in the subspaces with n ≤ nmax (nmax ∝ N ) electrons, we calculate the square of the total spin in the ground state to discuss magnetic properties of the models. We have found that although for n < nmax the ground states contain fully polarized states, there is no finite region of electron

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... s n/N < 1 (N = N/3 or N = N/5) where ground-state ferromagnetism survives for N → ∞.