  A new element is proposed to play a role in the evolution of extrasolar
planetary systems: the tidal (or elliptical) instability. It comes from a
parametric resonance and takes place in any rotating fluid whose streamlines
are (even slightly) elliptically deformed. Based on theoretical, experimental
and numerical works, we estimate the growth rate of the instability for
hot-jupiter systems, when the rotation period of the star is known. We present
the physical process, its application to stars, and preliminary results
obtained on a few dozen systems, summarized in the form of a stability diagram.
Most of the systems are trapped in the so-called "forbidden zone", where the
instability cannot grow. In some systems, the tidal instability is able to
grow, at short timescales compared to the system evolution. Implications are
discussed in the framework of mis-aligned transiting systems, as the rotational
axis of the star would be unstable in systems where this elliptical instability
grows.
