With this award the principal investigator will continue his modelling of elliptical galactic systems and the analytical solution of the model problems. In particular, he will construct self-consistent models of elliptical galaxies by means of Staeckel potentials. The main reasons for using Staeckel potentials are that they allow the same major orbit families as those found from numerical simulations of realistic galactic models and they lead to mathematically tractable problems. The aspect of astronomy that most of us are familiar with involves the use of telescopes to make observations of stars and galaxies. Another aspect that is less well known involves the construction of mathematical models of celestial objects in order to gain a greater understanding of the physics of stellar systems. This research involves the construction and analysis of a model for elliptical galaxies by means of a potential that describes an interacting system of many bodies.