  Given a semilattice $X$ we study the algebraic properties of the semigroup
$\upsilon(X)$ of upfamilies on $X$. The semigroup $\upsilon(X)$ contains the
Stone-Cech extension $\beta(X)$, the superextension $\lambda(X)$, and the space
of filters $\phi(X)$ on $X$ as closed subsemigroups. We prove that
$\upsilon(X)$ is a semilattice iff $\lambda(X)$ is a semilattice iff $\phi(X)$
is a semilattice iff the semilattice $X$ is finite and linearly ordered. We
prove that the semigroup $\beta(X)$ is a band if and only if $X$ has no
infinite antichains, and the semigroup $\lambda(X)$ is commutative if and only
if $X$ is a bush with finite branches.
