A search for pair-produced leptoquarks has been performed using a
sample of $\mbox{e}^+\mbox{e}^-$ collision events collected by the
OPAL detector at LEP at $\mbox{e}^+\mbox{e}^-$ centre-of-mass
energies from 189 up to 209~GeV. The data sample corresponds to a
total integrated luminosity of about 596~pb$^{-1}$. The
leptoquarks were assumed to be produced via couplings to the
photon and the Z$^0$ and then to decay promptly into a lepton and
a quark. The simplifying assumption is made that couplings within
a single generation of leptons can exist. No evidence for
contributions from leptoquark pair production processes was
observed. Lower limits at $95\%$ CL on scalar and vector
leptoquark masses are obtained. The existing limits are improved
for scalar leptoquarks with a large decay branching ratio to
quark-neutrino.