1. A method for address translation in a system running multiple levels of virtual machines containing a hierarchically organized translation lookaside buffer comprising at least two linked hierarchical sub-units, a first sub-unit comprising a lookaside buffer for some higher level address translation levels, and the second sub-unit comprising a lookaside buffer for some lower level address translation levels, and said second sub-unit being arranged to store TLB index address information of the upper level sub-unit as tag information in its lower level TLB structure, comprising the steps of collecting intermediate address translation results on different virtual machine levels; buffering the intermediate translation results in the translation lookaside buffer.