Systems Center Inc., the Vienna-based computer networking and software company, said yesterday that it expected to report a multimillion-dollar loss in the second quarter and that its president, John Barry, had resigned.

Trading in the company's stock on the New York Stock Exchange was delayed for nearly two hours yesterday morning as sell orders overwhelmed buying demand. When it finally opened for trading, Systems Center plunged $5.50 to $16.50 a share before rebounding to close its chaotic day at $17.87 1/2.

Kevin McNerney, Systems Center executive vice president, said the approximately $5 million to $6 million in losses expected for the quarter were largely related to difficulties in completing a pair of software-related acquisitions. He predicted that results would improve in the second half of the year.

"We knew we were in for a bumpy quarter, but we didn't know it would bring this kind of operating results," McNerney said.

McNerney said Barry's resignation was not related to the disappointing earnings. Instead, he said, Barry resigned after his hopes of becoming the company's chairman were dashed by Robert Cook, Systems Center chairman and chief executive officer, who let Barry know in recent months that he intended to stay at the helm.

McNerney said that in addition to reporting an operating loss for the quarter of about $2.5 million, the company would post a one-time loss of $3 million from legal fees and other acquisition expenses. In the second quarter of 1989, the company earned $2 million.

Systems Center, which is best known for its operating software for IBM computers, said revenue for the second quarter was about $23 million, compared with $18.3 million for the comparable period last year.

Since last year, Systems Center has been in the process of acquiring Australian-based Software Development International Ltd. and Net/Master, a software product that helps different computers work together. Systems Center last month completed the acquisitions, paying with its own shares. "That uncertainty {for the quarter} is behind them now," said Gibbs Moody, a senior technology analyst at Hambrecht & Quist in San Francisco. "The important point now is that what they have in-house now is the superior product in the network management industry. That will be a growth area for the next three years."