  In the present work we analyze the g-essence model for the particular
Lagrangian: $L=R+2[\alpha X^n+\epsilon Y-V(\psi,\bar{\psi})]$. The g-essence
models were proposed recently as an alternative and as a generalization to the
scalar k-essence. We have presented the 3 types solutions of the g-essence
model. We reconstructed the corresponding potentials and the dynamics of the
scalar and fermionic fields according the evolution of the scale factor. The
obtained results shows that the g-essence model can describes the decelerated
and accelerated expansion phases of the universe.
