  In an earlier article the second author introduced three families of tube
domains in ${\mathbf C}^2$ with holomorphic automorphism group isomorphic to
${\mathbf R}\ltimes{\mathbf R}^2$ and envelope of holomorphy equal to ${\mathbf
C}^2$. In the present paper we show that every domain in each of these families
is Kobayashi-hyperbolic.
