  We study Fourier and Laplace transforms for Fourier hyperfunctions with
values in a complex locally convex Hausdorff space. Since any hyperfunction
with values in a wide class of locally convex Hausdorff spaces can be extended
to a Fourier hyperfunction, this gives simple notions of asymptotic Fourier and
Laplace transforms for vector-valued hyperfunctions, which improves the
existing models of Komatsu, B\"aumer, Lumer and Neubrander and Langenbruch.
