  Consider the functional equation ${\mathcal E}_1(f) = {\mathcal E}_2(f)
({\mathcal E})$ in a certain framework. We say a function $f_0$ is an
approximate solution of $({\mathcal E})$ if ${\mathcal E}_1(f_0)$ and
${\mathcal E}_2(f_0)$ are close in some sense. The stability problem is whether
or not there is an exact solution of $({\mathcal E})$ near $f_0$. In this
paper, the stability of derivations on Hilbert $C^*$-modules is investigated in
the spirit of Hyers--Ulam--Rassias.

Functional Analysis;Analysis of PDEs