In this thesis, we investigate the orbit control strategies of small satellites in Low Earth Orbits (LEO) where the disturbance effects are significant, in particular the nonspherical Earth and atmospheric drag effects. These orbits are not suitable to be controlled by using traditional ground-based control strategies which generally require high-thrust propulsion systems and other expensive resources, both onboard and in the ground segment. In order to react to those disturbances spontaneously and keep a small satellite at a pre-defined station using its limited resources, autonomous orbit control technology needs to be enabled. With the current advances in navigation and propulsion technology, as well as onboard computation systems, the only key issue that needs further investigations for practical implementation of an autonomous orbit operation system is the control algorithm. The orbit control strategies we investigate here are treated separately for each of the orbital control phases, i.e. orbit deployment and acquisition, orbit transfer and orbit maintenance. We present various forms of the solutions of the epicycle motion which allow us to treat each control problem according to the control requirements, nature of perturbations, control time scales and available resources. Although applied in different manners, the optimal low-thrust control scheme is a common aim for all control problems investigated here, as we mainly focus upon applications for low cost small satellites in LEO. The verifications of the strategies proposed in this thesis have been demonstrated not only via computer simulations, but also successfully demonstrated on in-orbit small satellite platforms thanks to an active small satellite programme at Surrey Space Centre. The success of this study is hoped to provide a valuable basis for satellite orbit operations which will involve larger number of satellites with more complex configurations in the future.