  We study differential-difference equation of the form $$
\frac{d}{dx}t(n+1,x)=f(t(n,x),t(n+1,x),\frac{d}{dx}t(n,x)) $$ with unknown
$t(n,x)$ depending on continuous and discrete variables $x$ and $n$. Equation
of such kind is called Darboux integrable, if there exist two functions $F$ and
$I$ of a finite number of arguments $x$, $\{t(n\pm k,x)\}_{k=-\infty}^\infty$,
${\frac{d^k}{dx^k}t(n,x)}_{k=1}^\infty$, such that $D_xF=0$ and $DI=I$, where
$D_x$ is the operator of total differentiation with respect to $x$, and $D$ is
the shift operator: $Dp(n)=p(n+1)$. Reformulation of Darboux integrability in
terms of finiteness of two characteristic Lie algebras gives an effective tool
for classification of integrable equations. The complete list of Darboux
integrable equations is given in the case when the function $f$ is of the
special form $f(u,v,w)=w+g(u,v)$.
