  In this paper, we characterize and classify the isoparametric hypersurfaces
with constant principal curvatures in the product spaces $
\mathbb{Q}^{2}_{c_{1}} \times \mathbb{Q}^{2}_{c_{2}}$, where
$\mathbb{Q}^{2}_{c_{i}}$ is a space form with constant sectional curvature
$c_{i}$, for $c_1 \neq c_2$.
