We study single vector leptoquark production at future gamma e and gamma p colliders. The production cross sections are calculated for both ye and yp collisions. Analytical expressions are derived for the differential cross sections including the case of anomalous vector LQ coupling, alpha, to the photon. We find that the cross sections for single production of vector LQs have a rather weak dependence on the parameter alpha. The discovery limits for the masses of vector LQs are obtained for both cases.