  Let $F:[0,T]\times\R^n\mapsto 2^{\R^n}$ be a continuous multifunction with
compact, not necessarily convex values. In this paper, we prove that, if $F$
satisfies the following Lipschitz Selection Property: \begin{itemize}
\item[{(LSP)}] {\sl For every $t,x$, every $y\in \overline{co} F(t,x)$ and
$\varepsilon>0$, there exists a Lipschitz selection $\phi$ of $\overline{co}F$,
defined on a neighborhood of $(t,x)$, with $|\phi(t,x)-y|<\varepsilon$.}
\end{itemize} then there exists a measurable selection $f$ of $ext F$\ such
that, for every $x_0$, the Cauchy problem $$ \dot x(t)=f(t,x(t)),\qquad\qquad
x(0)=x_0 $$ has a unique Caratheodory solution, depending continuously on
$x_0$. We remark that every Lipschitz multifunction with compact values
satisfies (LSP). Another interesting class, for which (LSP) holds, consists of
those continuous multifunctions $F$ whose values are compact and have convex
closure with nonempty interior.
