The problem of restoring the equivalence between Light-Front (LF) Hamiltonian and conventional Lorentz-covariant formulations of gauge theories is solved for QED(1+1) and (perturbatively to all orders) for QCD(3+1). For QED(1+1) a LF Hamiltonian is constructed which reproduces the results of a Lorentz-covariant theory. This is achieved through bosonization of the model and by analyzing the resulting bosonic theory to all orders in the fermion mass. For QCD(3+1) we describe nonstandard regularization that allows to restore the mentioned equivalence with a finite number of counterterms in the LF Hamiltonian.