  Using numerical methods we thoroughly investigate the dynamical stability in
the region between the two planets found in HD 74156. The two planets with
minimum masses 1.56 M_JUP (HD 74156b) and 7.5 M_JUP (HD 74156c), semimajor axes
0.276 AU and 3.47 AU move on quite eccentric orbits (e=0.649 and 0.395). There
is a region between 0.7 and 1.4 AU which may host additional planets which we
checked via numerical integrations using different dynamical models. Besides
the orbital evolution of several thousands of massless regarded planets in a
three-dimensional restricted 4-body problem (host star, two planets + massless
bodies) we also have undertaken test computation for the orbital evolution for
fictive planets with masses of 0.1, 0.3 and 1 M_JUP in the region between
HD74156b and HD74156c. For direct numerical integrations up to 10^7 years we
used the Lie-integrator, a method with adaptive stepsize; additionally we used
the Fast Lyapunov Indicators as tool for detecting chaotic motion in this
region. We emphasize the important role of the inner resonances (with the outer
planet) and the outer resonances (with the inner planet) with test bodies
located inside the resonances. In these two "resonance" regions almost no
orbits survive. The region between the 1:5 outer resonance (0.8 AU) and the 5:1
inner resonance (1.3 AU), just in the right position for habitability, is also
very unstable probably due to three-body-resonances acting there. Our results
do not strictly "forbid" planets to move there, but the existence of a planet
on a stable orbit between 0.8 and 1.3 AU is unlikely.
