  We show the possibility of achieving experimentally a Takens-Bogdanov
bifurcation for the nonlinear interaction of two transverse modes ($l = \pm 1$)
in a $CO_2$ laser. The system has a basic O(2) symmetry which is perturbed by
some symmetry-breaking effects that still preserve the $Z_2$ symmetry. The
pattern dynamics near this codimension two bifurcation under such symmetries is
described. This dynamics changes drastically when the laser properties are
modified.
