An information processing system comprising two processing cores, the execution of an application by the system including the execution of application tasks and the execution of system tasks, the system comprising a micro-kernel executing the system tasks which are directly linked to hardware resources, the processing system comprising: - an mN-TT computation part of the micro-kernel on a first core A executing system tasks relating to the switching of the tasks on the core A, including, for each task, the updating of a state indicating whether said task is executable or not, said state being included in an execution context associated with said task and gathering execution data of said task, said state being able to take: ∘ a value indicating that the task is ready; ∘ a value indicating that the task is idle; ∘ a value indicating that the task is errored; - an mN-ET control part of the micro-kernel on a second core O executing application tasks triggered by input/output interrupts and executing system tasks relating to the control of the task allocation order on the core A, said system tasks including the management: ∘ of an ordered list of the tasks that are ready, and/or; ∘ of an ordered list of the tasks that are idle, and/or; ∘ of a list of tasks that are errored; characterized in that the mN-ET control part and the mN-TT computation part of the micro-kernel share said ordered lists of tasks, the order of the lists being maintained by the mN-ET control part and the content of each element of the lists being maintained by the mN-TT part, and in that the system tasks executed by the core A relating to the switching of the tasks include the updating within the context of executing each task: - of a limit date for the earliest start of execution and/or of a limit date for the latest end of execution; - of a remaining execution time quota; the core O ordering the tasks in the list of the tasks that are ready according to an order which makes it possible to execute each task according to the limit dates for the execution of each task and for the execution time quota of each task. - an mN-TT computation part of the micro-kernel on a first core A executing system tasks relating to the switching of the tasks on the core A, including, for each task, the updating of a state indicating whether said task is executable or not, said state being included in an execution context associated with said task and gathering execution data of said task, said state being able to take: ∘ a value indicating that the task is ready; ∘ a value indicating that the task is idle; ∘ a value indicating that the task is errored; ∘ a value indicating that the task is ready; ∘ a value indicating that the task is idle; ∘ a value indicating that the task is errored; - an mN-ET control part of the micro-kernel on a second core O executing application tasks triggered by input/output interrupts and executing system tasks relating to the control of the task allocation order on the core A, said system tasks including the management: ∘ of an ordered list of the tasks that are ready, and/or; ∘ of an ordered list of the tasks that are idle, and/or; ∘ of a list of tasks that are errored; characterized in that the mN-ET control part and the mN-TT computation part of the micro-kernel share said ordered lists of tasks, the order of the lists being maintained by the mN-ET control part and the content of each element of the lists being maintained by the mN-TT part, and in that the system tasks executed by the core A relating to the switching of the tasks include the updating within the context of executing each task: ∘ of an ordered list of the tasks that are ready, and/or; ∘ of an ordered list of the tasks that are idle, and/or; ∘ of a list of tasks that are errored; characterized in that the mN-ET control part and the mN-TT computation part of the micro-kernel share said ordered lists of tasks, the order of the lists being maintained by the mN-ET control part and the content of each element of the lists being maintained by the mN-TT part, and in that the system tasks executed by the core A relating to the switching of the tasks include the updating within the context of executing each task: - of a limit date for the earliest start of execution and/or of a limit date for the latest end of execution; - of a remaining execution time quota;