A generalized linear sigma model with two chiral nonets, one with a quark-antiquark structure, the other one with a four quark composition may describe adequately in the effective Lagrangian approach the light meson spectroscopy and interactions. In this talk we will discuss how this model may be improved by adding scalar and pseudoscalar glueballs based on the axial and trace anomalies. The decoupling limit is studied in detail and the mass spectrum is obtained. The SU(3)_V case is mentioned briefly. In all these cases the low energy spectroscopy is consistent with a picture in which the lighter pseudoscalar octet is mainly of a quark-antiquark structure whereas the lightest scalar octet is mainly a four quark structure. For the singlets in ascending order of the masses the pseudoscalars are mainly quark-antiquark, four quark and glue components whereas the scalars are four quark structures, quark-antiquark and glue.