This paper concerns the bifurcation properties of a model of a frequency modulated CO 2 laser in the form of a two-dimensional ordinary differential equation with a parametric periodic excitation. These properties are related to the bifurcation curves organization (structure) in a parameter plane (amplitude, frequency of the modulation). Two basic bifurcation structures appear, one concerning the higher harmonic solutions, the other the subharmonic solutions. Qualitative changes of these structures are considered when a third parameter (pump parameter) is varied.