  In a recent paper, M. E. Kahoui and M. Ouali have proved that over an
algebraically closed field $k$ of characteristic zero, residual coordinates in
$k[X][Z_1,\dots,Z_n]$ are one-stable coordinates. In this paper we extend their
result to the case of an algebraically closed field $k$ of arbitrary
characteristic. In fact, we show that the result holds when $k[X]$ is replaced
by any one-dimensional seminormal domain $R$ which is affine over an
algebraically closed field $k$. For our proof, we extend a result of S. Maubach
giving a criterion for a polynomial of the form $a(X)W+P(X,Z_1,\dots,Z_n)$ to
be a coordinate in $k[X][Z_1,\dots,Z_n,W]$.
  Kahoui and Ouali had also shown that over a Noetherian $d$-dimensional ring
$R$ containing $Q$ any residual coordinate in $R[Z_1,\dots,Z_n]$ is an
$r$-stable coordinate, where $r=(2^d-1)n$. We will give a sharper bound for $r$
when $R$ is affine over an algebraically closed field of characteristic zero.
