An address translation facility is provided for multiple virtualization levels, where a guest virtual address may be translated to a guest non-virtual address, the guest non-virtual address corresponding without translation to a host virtual address, and the host virtual address may be translated to a host non-virtual address, where translation within a virtualization level may be specified as a sequence of accesses to address translation tables. The address translation facility may include a first translation engine and a second translation engine, where the first and second translation engines each have capacity to perform address translation within a single virtualization level of the multiple virtualization levels. In operation, based on the first translation engine performing a guest level translation, the second translation engine may perform a host level translation of a resulting guest non-virtual address to a host non-virtual address based on the guest level translation by the first translation engine.