  We study the moduli space of coherent systems in $P^2$ using the Segre
invariant. We obtain necessary conditions for the existence of
$\alpha$-semistable coherent systems $(E,V)$ of type $(2, c_1, c_2, k)$, with
$k \geq 2$. Afterwards, we give numerical conditions to the nonemptiness of the
moduli space and compute the critical values depending of the Chern classes.
Finally, we give some topological properties of the flips.
