  A multiple-valued function $f:X\to {\bf Q}_Q(Y)$ is essentially a rule
assigning $Q$ unordered and non necessarily distinct elements of $Y$ to each
element of $X$. We study the Lipschitz extension problem in this context by
using two general Lipschitz extension theorems recently proved by U. Lang and
T. Schlichenmaier. We prove that the pair $(X,{\bf Q}_Q(Y))$ has the Lipschitz
extension property if $Y$ is a Banach space and $X$ is a metric space with a
finite Nagata dimension. We also show that ${\bf Q}_{Q}(Y)$ is an absolute
Lipschitz retract if $Y$ is a finite algebraic dimensional Banach space.
