  For given natural numbers $d_1,d_2$ let $\Omega_2(d_1,d_2)$ be the set off
all polynomial mappings $F=(f,g):\mathbb{C}^2\to\mathbb{C}^2$ such that deg
$f\le d_1$, deg $g\le d_2$. We say that the mapping $F$ is topologically stable
in $\Omega_2(d_1,d_2)$ if for every small deformation $F_t\in
\Omega_2(d_1,d_2)$ the mapping $F_t$ is topologically equivalent to the mapping
$F$. The aim of this paper is to characterize the topologically stable mappings
in $\Omega_2(d_1,d_2)$. In particular we show how to effectively determine a
member of $\Omega_2(d_1,d_2)$ with generic topology.
