A flurry of merger activity among some of the nation’s largest and most recognizable law firms is signaling that the once-booming legal industry is struggling to grow organically and instead turning to consolidation in hopes of grabbing new business.

Law firms announced 58 mergers in the first nine months of 2013, up 41 percent over the same period a year earlier, according to an October report from Altman Weil, a legal consulting group that tracks law firm mergers. Nineteen of them were proposed in the third quarter alone.

McKenna Long & Aldridge, an Atlanta-based firm whose strongest group is its government contracts practice in the District, is in talks to join the international law firm Dentons. Both firms completed their own mergers in the past 18 months: Dentons was the result of a merger between SNR Denton, Canadian firm Fraser Milner Casgrain and European firm Salans — creating one of the largest law firms in the world, with 2,500 attorneys and professionals in 52 countries — and McKenna Long merged with the California firm Luce, Forward, Hamilton & Scripps.

The Washington-based firm Dow Lohnes announced this month that 54 lawyers in its D.C. office will join Cooley, a 700-lawyer firm based in Silicon Valley, starting in January. San Francisco-based Orrick Herrington & Sutcliffe and New York-based Pillsbury Winthrop Shaw Pittman are also in talks to combine, a move that would form one of the biggest law firms in the United States, with about 1,700 lawyers. And reports emerged this week that Washington law and lobbying powerhouse Patton Boggs is seeking a merger with Texas-based firm Locke Lord.

Mergers are just one way that law firms are trying to recover and grow after being hit hard by the 2008 economic downturn, when companies dramatically scaled back on their outside legal spending. The pullback forced many large law firms to lay off lawyers en masse, restructure back-office operations and experiment with new ways of charging clients other than billing hourly, in order to appease companies’ demand for lower legal fees.

Many of the largest U.S. law firms are losing work to midsize firms willing to offer more flexible billing arrangements. A new report by LexisNexis found that legal fees paid by clients to firms with more than 750 lawyers shrank from 26 percent to 20 percent in the past three years. During the same period, firms with 201 to 500 lawyers saw their portion grow to 22 percent from 18 percent, according to the report, which analyzed more than 2 million invoices that outside law firms billed their corporate clients. The invoices covered more than 300,000 matters valued at more than $10 billion in legal fees.

Midsize firms are facing their own pressures. Some have decided that they need to expand beyond their regional footprints to attract big-name clients that are whittling down the number of outside law firms they work with, legal experts said.

“Some firms are bulking up so that they can be on the short list for the larger company assignments, because their size and geographic scope can be attractive in the situations where companies are looking to eliminate counsel,” said Steve Nelson, managing principal for the law and government affairs group at the McCormick Group, an executive search firm based in Arlington.

At the same time, the growing interconnectedness of the global economy has firms looking for new international alliances. But such marriages can be risky; some firms that went on expansion sprees before the recession quickly unraveled, contributing to the high-profile breakups of Howrey and Dewey & LeBoeuf.

“The economic picture for law firms continues to be uncertain at best,” Nelson said.