  The process e+ e- -> e+ e- Z/gamma* is studied with the OPAL detector at LEP
at a centre of mass energy of sqrt(s) = 189 GeV. The cross-section times the
branching ratio of the Z/gamma* decaying into hadrons is measured within
Lorentz invariant kinematic limits to be (1.2 +/- 0.3 +/- 0.1) pb for invariant
masses of the hadronic system between 5 GeV and 60 GeV and (0.7 +/- 0.2 +/-
0.1) pb for hadronic masses above 60 GeV. The differential cross-sections of
the Mandelstam variables s-hat, t-hat, and u-hat are measured and compared with
the predictions from the Monte Carlo generators grc4f and PYTHIA. From this,
based on a factorisation ansatz, the total and differential cross-sections for
the subprocess e gamma -> e Z/gamma* are derived.
