A method for memory virtualization for systems with processors which offer virtualization support, the virtualization support not having a second level address translation, SLAT, wherein the system comprises at least the guest virtual, guest physical and host physical address spaces, and wherein the system further comprises: a guest pagetable for translating addresses of the guest virtual address space into addresses of the guest physical address space, a shadow pagetable for translating addresses of the guest virtual address space into addresses of the host physical address space, wherein a guest operating system does not have access to the shadow pagetable, and a hypervisor which is configured for calculating address entries for the shadow pagetable from respectively valid address entries in the guest pagetable, and for entering said calculated address entries for the shadow pagetable into the shadow pagetable, managing one or more shadow pagetables by the hypervisor while the guest context is executed by the guest operating system, wherein the number of the one or more shadow pagetables is smaller than or equal to the number of guest contexts in the current working set, recording the modifications of the guest pagetables in a queue, wherein after exhaustion of the capacity of the queue or when the guest operating system is changing from the kernel mode to the user mode, the hypervisor is informed about the modifications of the guest pagetables which have been performed so far and which are recorded in the queue, the hypervisor updates the one or more shadow pagetables in accordance with the modifications recorded in the queue by iterating over all queue entries, and the processors are configurable to transmits a guest pagefault to the kernel of the guest operating system directly, without intervention of the hypervisor; characterized in that the pagefault treatment routine of the guest operating system is configured such that in a situation in which a shadow pagetable which was previously bound to a guest context had its content discarded when the memory virtualization exceeds its memory allotment predetermined by the hypervisor, and wherein a pagefault occurred in the guest operating system due to the no longer present shadow pagetable content, the pagefault treatment routine calls the hypervisor, wherein the hypervisor is configured such that after having been called by the pagefault treatment routine in a situation in which a shadow pagetable which was previously bound to a guest context had its content discarded and wherein a pagefault occurred in the guest operating system due to the no longer present shadow pagetable content, the hypervisor updates the shadow pagetable. a guest pagetable for translating addresses of the guest virtual address space into addresses of the guest physical address space, a shadow pagetable for translating addresses of the guest virtual address space into addresses of the host physical address space, wherein a guest operating system does not have access to the shadow pagetable, and a hypervisor which is configured for calculating address entries for the shadow pagetable from respectively valid address entries in the guest pagetable, and for entering said calculated address entries for the shadow pagetable into the shadow pagetable, managing one or more shadow pagetables by the hypervisor while the guest context is executed by the guest operating system, wherein the number of the one or more shadow pagetables is smaller than or equal to the number of guest contexts in the current working set, recording the modifications of the guest pagetables in a queue, wherein after exhaustion of the capacity of the queue or when the guest operating system is changing from the kernel mode to the user mode, the hypervisor is informed about the modifications of the guest pagetables which have been performed so far and which are recorded in the queue, the hypervisor updates the one or more shadow pagetables in accordance with the modifications recorded in the queue by iterating over all queue entries, and the processors are configurable to transmits a guest pagefault to the kernel of the guest operating system directly, without intervention of the hypervisor; characterized in that the pagefault treatment routine of the guest operating system is configured such that in a situation in which a shadow pagetable which was previously bound to a guest context had its content discarded when the memory virtualization exceeds its memory allotment predetermined by the hypervisor, and wherein a pagefault occurred in the guest operating system due to the no longer present shadow pagetable content, the pagefault treatment routine calls the hypervisor, wherein the hypervisor is configured such that after having been called by the pagefault treatment routine in a situation in which a shadow pagetable which was previously bound to a guest context had its content discarded and wherein a pagefault occurred in the guest operating system due to the no longer present shadow pagetable content, the hypervisor updates the shadow pagetable.