This research work focuses on the selection, development and testing of orbit prediction and orbit determination methods: the selection is carried out for the purpose of space object catalogue maintenance. Approximations in the selected propagator method and uncertainties in the selected force models are studied. Methods for uncertainty propagation are investigated. The first objective of this study is to find a propagation method that can be used for several cataloguing tasks, and will offer a favourable trade-off between accuracy and computational effort. The selected propagation method should be a computationally lean alternative to the more common numerical orbit propagation techniques. As a second objective, efforts were concentrated in characterising the model uncertainties and in formulating a method to capture these uncertainties within the propagated covariances.