PURPOSE: To delete the data set with an end indication given from a TSS terminal device by holding temporarily a data set deleting indication given from said terminal device for a host computer and then deleting artificially the data set designated to the terminal device.

CONSTITUTION: The section data set of a data set memory part 13 of a host computer is divided into several areas (members), and the address of each member is stored in a directory part. In case only a member AA2 is deleted out of the section data set and only a data set name AAA is designated with no designation of member names, a data set deletion control part 31 does not execute immediately but holds the received deletion command and the name AAA. A mask part functions as if it deleted artificially the access given from an access control part. Therefore it is impossible for an operator to process the next member AA1. Thus a command is delivered to invalidate the preceding command, and the retained command is invalidated. Then a session end command is supplied for execution of deletion of the data set.