  We extend the k_\perp-factorization formalism for exclusive photoproduction
of vector mesons to the production of electroweak Z^0 bosons. Predictions for
the gamma p \to Z^0 p and p p \to p p Z^0 reactions are given using an
unintegrated gluon distribution tested against deep inelastic data. We present
distributions in the Z^0 rapidity, transverse momentum of Z^0 as well as in
relative azimuthal angle between outgoing protons. The contributions of
different flavours are discussed. Absorption effects lower the cross section by
a factor of 1.5-2, depending on the Z-boson rapidity. We also discuss the
production of Z^0 bosons in central inclusive production. Here rapidity and
(x_{\Pom,1}, x_{\Pom,2}) distributions of Z^0 are calculated. The corresponding
cross section is about three orders of magnitude larger than that for the
purely exclusive process.
