  The scalar and vector leptoquark pair production cross sections in hadronic
collisions are calculated. In a model independent analysis we consider the most
general C and P conserving couplings of gluons to both scalar and vector
leptoquarks described by an effective low--energy Lagangian which obeys SU(3)_c
invariance. Analytrical expressions are derived for the differential and
integral scattering cross sections including the case of anomalous vector
leptoquark couplings, $\kappa_G$ and $\lambda_G$, to the gluon field. Numerical
predictions are given for the kinematic range of the TEVATRON and LHC. The pair
production cross sections are also calculated for the resolved photon
contributions to $ep \rightarrow e \overline{\Phi} \Phi X$ at HERA and LEP
$\otimes$ LHC, and for the process $\gamma \gamma \rightarrow \Phi \overline
{\Phi}X$ at possible future $e^+e^-$ linear colliders and $\gamma \gamma$
colliders. Estimates of the search potential for scalar and vector leptoquarks
at present and future high energy colliders are given.
