  It is well-known that every derivation of a semisimple Lie algebra $L$ over
an algebraically closed field $F$ with characteristic zero is inner. The aim of
this paper is to show what happens if the characteristic of $F$ is prime with
$L$ an exceptional Lie algebra. We prove that if $L$ is a Chevalley Lie algebra
of type $\{G_2,F_4,E_6,E_7,E_8\}$ over a field of characteristic $p$ then the
derivations of $L$ are inner except in the cases $G_2$ with $p=2$, $E_6$ with
$p=3$ and $E_7$ with $p=2$.
