  The algebraic approach to operator perturbation method has been applied to
two quantum--mechanical systems ``The Stark Effect in the Harmonic Oscillator''
and ``The Generalized Zeeman Effect''. To that end, two realizations of the
superoperators involved in the formalism have been carried out. The first of
them has been based on the Heisenberg--Dirac algebra of $\hat{a}^\dagger$,
$\hat{a}$, $\hat{1}$ operators, the second one has been based in the angular
momemtum algebra of $\hat{L}_+$, $\hat{L}_-$ and $\hat{L}_0$ operators. The
successful results achieved in predicting the discrete spectra of both systems
have put in evidence the reliability and accuracy of the theory.
