Constructing deliberative real-time AI systems is challenging due to the high execution-time variance in AI algorithms and the requirement of worst-case bounds for hard real-time guarantees, often resulting in poor use of system resources. Using a motivating case study based on RoboCup, the general problem of resource usage maximization in a real-time AI agent is addressed.In this thesis it was shown that by employing a hybrid task model, for imprecise computation of the form "Prologue-Optional-Epilogue", a variety of AI algorithms with different hard and optional (anytime) timing requirements can be supported. An exact schedulability, based on a simple offset between the Prologue and Epilogue components, is devised but shown to be computationally prohibitive when a large number of imprecise tasks are present. For this reason, a tractable sufficient schedulability test was also devised, inspired by Tindell's analysis, where the time complexity of calculating the busy period of each task is reduced from O(2 n ) to O(2n).Further, with a novel scheduling scheme based on Dual Priority Scheduling, schedulability can be guaranteed for the hard Prologue and Epilogue tasks while the latter can be delayed as much as possible for allowing optional and anytime components to be executed for enhancing system utility. Suggestions on how aperiodic tasks can be scheduled effectively within the framework and how tasks can be prioritized based on their utilities by an efficient algorithm are also provided.The works presented in this thesis provide new advances in fixed priority response time analysis for imprecise computation which, together with present results in the literature, should provide a more comprehensive scheduling framework where real-time AI systems can be suitably supported.i