A multiprogramming/multiprocessing computer system for executing a plurality of processes sharing common information in the form of records, pages or messages, employing an apparatus for avoiding an interference between two processes seeking access to elements of common information. The system operates to store in a first memory utilization data in table form identifying the processes which have accessed each individual element of common information. A second memory stores a matrix of precedence data representing the relative order in which processes must access the common information in accordance with a predetermined set of access rules. When a first process enters a request to access an element of common information, the system identifies from the utilization table any other process which, according to the access rules, must be given precedence to the common information over the first process. Thereafter, the system inspects the second memory and determines from the precedence data therein whether any inverse precedence relationships have been detected and, if so, rejects the access request entered by the first process and moves on to process the next access request.