E-Trade Group Inc. plans to offer after- hours trading through Instinet, the busiest market for buying and selling stocks when regular exchanges are closed.

The service, set to begin next month, would make E-Trade the biggest online broker so far to let its customers react to late- breaking news, a privilege long enjoyed by money managers, mutual funds and other institutional investors.

While most brokers are expected to offer some form of after-hours trading in the near future, the alliance announced yesterday may hasten the latest chapter in an online trading revolution that’s remaking the way Wall Street does business.

Everybody else is playing catch-up with us, said E-Trade Chief Executive Officer Christos Cotsakos.

E-Trade won’t be providing its 1.3 million customers with the same round-the-clock trading access that Instinet gives major investors — at least not at first.

The after-hours session will run for 2 1/2 hours following the regular 4 p.m. close of NYSE and Nasdaq trading, about an hour longer than the after-hours session offered by Datek Online Holdings on the Island ECN system.

If nothing else, E-Trade’s move may force a response from Charles Schwab, the top Web broker with 2.8 million active accounts holding $250 billion in assets.

Schwab recently formed a partnership with Fidelity Investments and Donaldson, Lufkin & Jenrette to create an electronic market. The new market would likely provide the forum for after-hours trading at those firms, but no formal plans have been announced.

By offering after-hours trading through Instinet, a unit of Reuters Group PLC. E- Trade is bringing its customers a safer way to take part in a volatile market where stock prices can swing wildly due to an imbalance of buy and sell orders.

Instinet prices definitely aren’t immune to those swings. However, thanks to its large base of institutional clients, Instinet’s after- hours volume already averages 20 million shares a day, making it easier to balance the orders on both sides of a trade.

The magic of getting retail investors the best possible prices is to have their orders interact with the institutional order flow, Douglas Atkin. chief executive of Instinet, said in an interview. The best way to decrease volatility is to build liquidity. We are by far the largest pool of liquidity.

Without Instinet’s volume, newer after- hours markets like Island ECN may have a harder time stabilizing prices. That’s why most of the after-hours ventures announced so far are making investors name a specific price at which to buy or sell a stock.

But E-Trade, more confident about the stability of Instinet trading, is not requiring so-called limit orders.

E-Trade’s new service also may have an advantage because many of the newer after- hours markets only trade stocks listed on the Nasdaq Stock Market. while Instinet also handles New York Stock Exchange issues, such as the 30 companies in the Dow Jones industrial average.

The relationship with Instinet is exclusive through the end of 1999, at which time Instinet would be free to strike deals with other brokerages. Rather than offering an evening session like the post-commute, post-dinner trading planned by rivals such as MarketXT, the next step for E-Trade may be a pre-market session in the morning, Cotsakos said.

E-Trade will charge its regular commission rates for the new service, which follows a recent announcement by America Online Inc. that the world’s biggest Internet service will be offering its 18 million members access to after-hours trading through Wit Capital later this year.

Several of the new after-hours systems boast major partners, all of them anxious to grab a share of a new market they hope will be as explosive as online trading. E-Trade and Instinet are both partners in a new trading network named Archipelago, along with Goldman Sachs and J.P. Morgan. Goldman Sachs also owns a stake in Wit Capital. Datek’s Island subsidiary is partially owned by Waterhouse.

All the impending competition has prompted the NYSE and the Nasdaq Stock Market to announce that they’ll introduce their after-hours trading sessions sometime next year.