Two of the largest independent U.S. high-frequency-trading firms are in early merger discussions, as a downturn in trading opportunities has spurred cutbacks and tie-up talks among rivals.

RGM Advisors LLC and Allston Trading LLC have discussed a deal that would combine their respective strengths in automated stock trading and futures markets, according to people close to the talks.

New technologies have fueled a surge in computer-driven, rapid-fire trading over the past decade, boosting the profile of independent, proprietary "prop shops" that trade for their own benefit, while also prompting big banks to embrace high-frequency techniques.

High-frequency traders use sophisticated hardware and mathematical models to rapidly buy and sell securities and other instruments on exchanges around the world, pocketing profits on often-tiny shifts in prices.

While fast trading benefited from the opportunities churned up by the market volatility of 2008 and 2009, a downturn in volumes on both sides of the Atlantic since then has squeezed profits, spurred cutbacks and set the stage for industry consolidation. Meanwhile, regulators are drawing up tighter restrictions on automated-trading practices, and some trading venues are clamping down on high-speed dealing.

The potential combination of Austin, Texas-based RGM and Chicago-based Allston could create a more-diversified trading group with lower expenses. A deal could encourage other traders to pursue tie-ups as a way to diversify their businesses and spread the costs of monitoring risks and connecting to exchanges.

Discussions are at an early stage, according to people with knowledge of the talks. The discussions could end with no deal, these people said.

"From time to time, as interesting partnership opportunities emerge or as we identify acquisition opportunities, Allston management will of course consider them if they accelerate our growth objectives but will not comment on any of those discussions unless there is something concrete to communicate," said Allston Chief Executive Raj Mahajan in a statement.

Richard Gorelick, CEO of RGM, said in a statement his firm doesn't publicly comment on speculation about potential deals. "We are focused on continuing to grow our business in a variety of ways," he said.

Jefferies Group LLC is advising Allston, while RGM hasn't retained a bank in the discussions, according to people familiar with the talks.

The two privately held firms are major customers of the New York Stock Exchange and futures platforms operated by CME Group Inc. (CME), and a deal would extend a string of tie-ups as electronic traders combine or consider selling out to better-capitalized rivals.

Automated traders' push to trade more assets across more markets has slowed as firms have cut jobs and operations to stay competitive with a growing number of competitors pursuing electronic strategies. Chicago-based trading groups including Getco, Sun Holdings LLC and Infinium Capital Management LLC have shed staff and named new chief executives who are seen open to expansion through deal-making.

Getco LLC, a big high-frequency market maker, has acquired several smaller firms and in December agreed to buy Jersey City-based Knight Capital Group Inc. after that firm was hobbled by faulty trading software.

"The dialogues have picked up post-Knight," said Chris Malo, chief financial officer of Sun. "We're in accelerated growth mode, both organically and inorganically."

Private firms' tendency to closely guard their trading methods, even in talks with potential partners, has been a hurdle to deal-making, however. "It's very difficult to get two firms to get comfortable with one another," said Jeff Bell, chief executive of Lime Brokerage LLC, which provides technology to electronic traders.

U.S. stock-trading volumes have declined in each of the past three years and this year are running 35% below the industry's peak in 2009, when an average 9.8 billion shares changed hands a day, according to Sandler O'Neill + Partners. Activity on U.S. futures exchanges this year has rebounded from a slower 2012, but it has waxed and waned since the 2008 financial crisis.

"High-frequency trading in general is a volume business," said Robert Stowsky, a senior analyst with Aite Group, a Boston-based firm that researches electronic trading. "If trading volumes are going down, that means it's tougher for prop shops to make money."

The slowdown has forced some high-speed specialists to leave the business. One notable casualty was Eladian Partners LLC, a venture founded by former Citigroup Inc. (C) trading executives and backed by private-equity firm Technology Crossover Ventures. Eladian closed in October after TCV opted not to add to its investment, people familiar with the matter have said.

RGM was founded in 2001 and uses complex computer models to place opportunistic trades, mainly on U.S. and European stock markets. The firm employs about 130 staff in Austin and London and is seen complementing Allston's specialty in providing liquidity to futures markets. Allston, which was founded in 2003, has about 150 employees in Chicago and London.

Both firms have hired staff in recent months, and Mr. Mahajan said Allston is pursuing a strategy to double the firm's net trading revenue.

Write to Jacob Bunge at jacob.bunge@wsj.com

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