Article révisé par les pairs
Résumé : The purpose of this paper is to show that the determination of the symmetry Lie algebra of a Hamiltonian with accidental degeneracy is more a matter of art than science, in the usual sense of these two words. Our thesis is defended through examples in which the Hamiltonians are linear combinations of the number operator N and the angular momentum M of a two dimensional oscillator. The standard approach to the problem when H = N or M, fails for H = N ± M or H = N ±