A method to perform a least recently used (LRU) algorithm for a co-processor is described, which co-processor in order to directly use instructions of a core processor and to directly access a main storage by virtual addresses of said core processor comprises a TLB for virtual to absolute address translations plus a dedicated memory storage also including said TLB, wherein said TLB consists of at least two zones which can be assigned in a flexible manner more than one at a time. Said method to perform a LRU algorithm is characterized in that one or more zones are replaced dependent on an actual compression service call (CMPSC) instruction.