  We have derived the invariants of cosmological models with Gurzadyan-Xue dark
energy, along with the solutions for any time dependent light speed and
gravitational constant. The correspondence of the invariants with the
separatrices found earlier for the GX-models in \cite{Ver06a} is shown, and
hence the basis of then detected hidden symmetry is now revealed. Solutions are
derived both for radiation and matter models, as well as with both components.
It is interesting that, the solutions for the scale factor do not depend on the
gravitational constant but only on the 'time evolution' of the speed of light.
GX-invariants act as efficient tools describing the models and the phases of
the cosmological expansion.
