The companies tried to wear each other out in what was then called the midrange server market. The DEC VAX, rolled out in 1976 was a legend but the IBM System /36s and /38s were no slouches. Big Blue morphed those successful servers into its VAX killer, the AS/400 in 1988 and by 1994, 250,000 of them had been sold. DEC eventually tried to counter with its Alpha chip -based line of advanced servers but by the early 1990's Ken Olsen's engineering company was in trouble.
Meanwhile the companies' competed with their network technologies as well - DEC's DECnet and IBM's Systems Network Architecture - both being introduced in 1974. While the general perception at the time was that DECnet generally held sway with the techie folks and IBM's SNA went after the business side of the house, that distinction was ultimately lost by onrushing industry clamor for less proprietary technology, namely TCP/IP. Download the latest Network World Executive Guide - Growing a Data Center For a Growing Business
The combination of bad results and industry acceptance of IP ultimately knocked DEC out and it was sold to Compaq in 1998 for $9.6 billion. IBM fared only a little better in the network arena, but SNA ultimately wilted. IBM sold good portions of its network business in 1999 to a new, more ravenous rival: Cisco.