The orbital structure of triaxial models with weak central density cusps , \rho \propto r ^ { - \gamma } , \gamma < 1 , is investigated .
The stability of the x - ( long- ) axis orbit – and hence the existence of box orbits – depends sensitively on \gamma ; the range of model shapes for which the x -axis orbit is stable becomes progressively smaller as \gamma approaches one .
The banana and fish boxlets in the x - z ( long axis–short axis ) plane are stable over a wide range of model parameters .
The boxlets in the x - y and y - z planes are generally vertically unstable .