  For a commutative C*-algebra $\mathcal A$ with unit $e$ and a
Hilbert~$\mathcal A$-module $\mathcal M$, denote by End$_{\mathcal A}(\mathcal
M)$ the algebra of all bounded $\mathcal A$-linear mappings on $\mathcal M$,
and by End$^*_{\mathcal A}(\mathcal M)$ the algebra of all adjointable mappings
on $\mathcal M$. We prove that if $\mathcal M$ is full, then each derivation on
End$_{\mathcal A}(\mathcal M)$ is $\mathcal A$-linear, continuous, and inner,
and each 2-local derivation on End$_{\mathcal A}(\mathcal M)$ or
End$^{*}_{\mathcal A}(\mathcal M)$ is a derivation. If there exist $x_0$ in
$\mathcal M$ and $f_0$ in $\mathcal M^{'}$, such that $f_0(x_0)=e$, where
$\mathcal M^{'}$ denotes the set of all bounded $\mathcal A$-linear mappings
from $\mathcal M$ to $\mathcal A$, then each $\mathcal A$-linear local
derivation on End$_{\mathcal A}(\mathcal M)$ is a derivation.
