  We consider the tidal interaction of a fully convective primary star and a
point mass. Using a normal mode decomposition we calculate the evolution of the
primary angular velocity and orbit for arbitrary eccentricity e. The
dissipation acting on the tidal perturbation is associated with convective
turbulence. A novel feature of the Paper is that, to take into account of the
fact that there is a relaxation time t_{c}, being the turn-over time of
convective eddies, associated with the process, this is allowed to act non
locally in time, producing a dependence of the dissipation on tidal forcing
frequency. Results are expressed in terms of the Fourier coefficients of the
tidal potential. We find analytical approximations for these valid for $e>0.2$.
When the tidal response is frequency independent, our results are equivalent to
those obtained in the standard constant time lag approximation. When there is
the frequency dependence of the dissipative response, the evolution can differ
drastically. In that case the system can evolve through a sequence of
spin-orbit corotation resonances with Omega_{r}/Omega_{orb}=n/2, where
Omega_{r} and Omega_{orb} are the rotation and orbital frequencies and n is an
integer. We study this case analytically and numerically.
