  We study the transmission eigenvalues for the multipoint scatterers of the
Bethe-Peierls-Fermi-Zeldovich-Beresin-Faddeev type in dimensions $d=2$ and
$d=3$. We show that for these scatterers: 1) each positive energy $E$ is a
transmission eigenvalue (in the strong sense) of infinite multiplicity; 2) each
complex $E$ is an interior transmission eigenvalue of infinite multiplicity.
The case of dimension $d=1$ is also discussed.
