In this thesis, we are interested in the real-time fixed-priority scheduling problem of energy-harvesting systems. An energy-harvesting system is a system that can collect the energy from the environment in order to store it in a storage device and then to use it to supply an electronic device. This technology is used in small embedded systems that are required to run autonomously for a very long lifespan. Wireless sensor networks and medical implants are typical applications of this technology. Moreover, most of these devices have to execute many recurrent tasks within a limited time. Thus, these devices are subject to real-time constraints where the correctness of the system depends not only on the correctness of the results but also on the time in which they are delivered. This thesis focuses on the preemptive fixed-task-priority real-time scheduling for such systems in monoprocessor platforms. The problematic here is to find efficient scheduling algorithms and schedulability conditions that check the schedulability of a given task set in a given energy configuration. The first result of this thesis is the proposition of the PFPasap scheduling algorithm. It is an adaptation of the classical fixed-task-priority scheduling to the energy-harvesting context. It consists of executing tasks as soon as possible whenever the energy is sufficient to execute at least one time unit and replenishes otherwise. The replenishment periods are as long as needed to execute one time unit. We prove that PFPasap is optimal but only in the case of non-concrete systems where the first release time of tasks and the initial energy storage unit level are known only at run-time and where all the tasks consume more energy than the replenishment during execution times. A sufficient and necessary schedulability condition for such systems is also proposed. Unfortunately, when we relax the assumption of tasks energy consumption profile, by considering both tasks that consume more energy than the replenishment and the ones that consume less than the replenishment, PFPasap is no longer optimal and the worst-case scenario is no longer the synchronous release of all the tasks, which makes the precedent schedulability test only necessary. To cope with this limitation, we propose to upper bound tasks worst-case response time in order to build sufficient schedulability conditions instead of exact ones. Regarding algorithms optimality, we explore different ideas in order to build an optimal algorithm for the general model of fixed-task-priority tasks by considering all types of task sets and energy consumption profiles. We show through some counter examples the difficulty of finding such an algorithm and we show that most of intuitive scheduling algorithms are not optimal. After that, we discuss the possibility of finding such an algorithm. In order to better understand the scheduling problematic of fixed-priority scheduling for energy-harvesting systems, we also try to explore the solutions of similar scheduling problematics, especially the ones that delay executions in order to guarantee some requirements. The thermal-aware scheduling is one of these problematics. It consists of executing tasks such that a maximum temperature is never exceeded. This may lead to introduce additional idle times to cool down the system in order to prevent reaching the maximum temperature. As a first step, we propose in this thesis to adapt the solutions proposed for energy-harvesting systems to the thermal-aware model. Thus, we adapt the PFPasap algorithm to respect the thermal constraints and we propose a sufficient schedulability analysis based on worst-case response time upper bounds. Finally, we present YARTISS: the simulation tool used to evaluate the theoretical results presented in this dissertation.