The work presented in this thesis is an experimental investigation into the sputtering of oxygen and water ice by 4 ke V ions under conditions existing in the Interstellar Medium (ISM). This work is divided into two main parts : 1) sputtering of oxygen ice by singly and doubly charged ions He+, Ar+, C+, N+ ,0, C2+, N2+ and 0 2+ and 2) sputtering of water ice by C+, N+, 0+, C2+, N2+ and 0 2+. The experimental sputter yield obtained for both oxygen and water ice is compared with those from a theoretical obtained model and found to be in reasonable agreement within the experimental errors. For oxygen and water ice, deposited at 10 K, the refractive index was experimentally determined and found to have values of 1.285 and 1.282 respectively that are in good agreement with previous results. In the case of oxygen ice the sputtering yields are at least nine times larger compared to that of water ice. For water ice the doubly charged ions have, the same sputtering yield ,as the singly charged ions within the experimental errors. In the case of oxygen ice the doubly charged ions have the same sputtering yield as the singly charged ions, except 0+ and 0 2+, where 0 2+ has a significantly lower sputtering yield.