The axial Rotation Vibration Model is here extended to describe also triaxial equilibrium shapes with beta and gamma vibrations allowing for the interaction between vibrations and rotations. This Triaxial Rotation Vibration Model (TRVM) is applied to Xe and Ba isotopes with mass numbers between 120 and 130. This area has recently been pointed out to be the O(6) limit of the Interacting Boson Approximation (IBA). The present work shows that the TRVM can equally well describe these nuclei concerning their excitation energies and E2 branching ratios.