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; and buffering the intermediate translation results in the translation lookaside buffer; wherein: the intermediate address translation results are used to bypass translations steps for subsequent translation requests for a slightly different virtual address; a caching scheme for frequently used table fetch data is handled differently from infrequently used table fetch data; and for translation steps which cannot be bypassed, the table fetch data are cached in a high-speed cache, and infrequently used table fetch data which are often bypassed, are cached in a low-speed cache.