  We construct examples of asymptotically cylindrical Riemannian 8-manifolds
with holonomy group Spin(7). To our knowledge, these are the first such
examples. The construction uses an extension to asymptotically cylindrical
setting of Joyce's existence result for torsion-free Spin(7)-structures. One
source of examples arises from `Fano-type' Kaehler 4-orbifolds with smooth
anticanonical Calabi-Yau 3-fold divisors and with compatible antiholomorphic
involution. We give examples using weighted projective spaces and calculate
basic topological invariants of the resulting Spin(7)-manifolds.
