  We consider solutions of the Stokes system in a neighborhood of a point in
which the velocity $u$ vanishes of order $d$. We prove that there exists a
divergence-free polynomial $P$ in $x$ with $t$-dependent coefficients of degree
$d$ which approximates the solution $u$ of order $d+\alpha$ for certain
$\alpha>0$. The polynomial $P$ satisfies a Stokes equation with a forcing term
which is a sum of two polynomials in $x$ of degrees $d-1$ and $d$. The results
extend to Oseen systems and to the Navier-Stokes equation.
