  We investigate the stability regions of hypothetical terrestrial planets
around the Lagrangian equilibrium points L4 and L5 in some specific extrasolar
planetary systems. The problem of their stability can be treated in the
framework of the restricted three body problem where the host star and a
massive Jupiter-like planet are the primary bodies and the terrestrial planet
is regarded as being massless. From these theoretical investigations one cannot
determine the extension of the stable zones around the equilibrium points.
Using numerical experiments we determined their largeness for three test
systems chosen from the table of the know extrasolar planets, where a giant
planet is moving close to the so-called habitable zone around the host star in
low eccentric orbits. The results show the dependence of the size and structure
of this region, which shrinks significantly with the eccentricity of the known
gas giant.
