  We study all possible $U(1)$-extensions of the standard model (SM) in the
framework of noncommutative geometry (NCG) with the algebra
$\hhh\op\cc\op\cc\op M_3(\cc)$. Comparison to experimental data about the mass
of a hypothetical $Z'$ gauge boson leads to the necessity of introducing at
least one new family of heavy fermions.
