This paper describes a new hypervisor built to run Linux in a virtual machine. This hypervisor is built inside Anaxagoros, a real-time microkernel designed to execute safely hard real-time and non real-time tasks. This allows the execution of hard real-time tasks in parallel with Linux virtual machines without interfering with the execution of the real-time tasks. We implemented this hypervisor and compared performances with other virtualization techniques. Our hypervisor does not yet provide high performance but gives correct results and we believe the design is solid enough to guarantee solid performances with its future implementation.