  Let $f$ and $g$ be Weierstrass polynomials with coefficients in the ring of
formal power series over an algebraically closed field of characteristic zero.
Assume that $f$ is irreducible and quasi-ordinary. We show that if degree of
$g$ is small enough and all monomials appearing in the resultant of $f$ and $g$
have orders big enough, then $g$ is irreducible and quasi-ordinary,
generalizing Abhyankar's irreducibility criterion for plane analytic curves.
