  The cross section for vector leptoquark production in electron--gluon
collisions is calculated analytically using the Lagrangian with the minimal
couplings between the leptoquarks and the gauge fields of the standard model.
It is found that the cross section significantly exceeds the corresponding
quantity previously presented in the literature. The cross section of exclusive
$W$ boson production in neutrino--photon scattering emerges as a by-product of
this letter. The obtained results can be used for studies at $ep$ colliders.
