A continuum is a compact connected metric space. Given a continuum $X$ and a positive integer $n$, let $C_n(X)=\{A\subset X\ |\ A\ \hbox{is nonempty and has at most $n$ components}\}$ and let $F_n(X)=\{A\in C_n(X)\ |\ A\ \hbox{has at most $n$ points}\}$ with the Hausdorff metric. The $n$-fold hyperspace suspension of $X$ is $HS_n(X)=C_n(X)/F_n(X)$ with the quotient topology. We will present examples and properties of these spaces.