  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 $n\le n_{\max}$ ($n_{\max}\propto N$) 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 $n<n_{\max}$ the ground states contain
fully polarized states, there is no finite region of electron densities
$n/{\cal{N}} <1$ (${\cal{N}}=N/3$ or ${\cal{N}}=N/5$) where ground-state
ferromagnetism survives for ${\cal{N}}\to\infty$.
