  The Blume - Emery - Griffiths model is investigated by use of the cluster
variation method in the pair approximation. We determine the regions of the
phase space where reentrant phenomenon takes place. Two regions are found,
depending on the sign of the reduced quadrupole - quadrupole coupling strength
$\xi$. For negative $\xi$ we find Para-Ferro-Para and Ferro-Para-Ferro-Para
transition sequences; for positive $\xi$, a Para$_-$-Ferro-Para$_+$ sequence.
Order parameters, correlation functions and specific heat are given in some
typical cases. By-products of this work are the equations for the critical and
tricritical lines.
