  We prove that if the $f$-sectional curvature at any point $p$ of a
$(2n+s)$-dimensional $f$-$(\kappa,\mu)$ manifold with $n>1$ is independent of
the $f$-section at $p$, then it is constant on the manifold. Moreover, we also
prove that an $f$-$(\kappa,\mu)$ manifold which is not an $S$-manifold is of
constant $f$-sectional curvature if and only if $\mu=\kappa+1$ and we give an
explicit expression for the curvature tensor field. Finally, we present some
examples.
