Construction unions, plagued by devastating losses to nonunion competition in recent years, have been so encouraged by a new organizing drive in Los Angeles that they are planning to extend the campaign soon to other metropolitan areas.

Among the possible new targets are Washington, D.C., and Baltimore, according to Robert A. Georgine, president of the AFL-CIO's Building and Construction Trades Department, which is spearheading the drive.

Since the Los Angeles campaign was started last March, more than 10,000 new members have been recruited, adding substantially to the construction unions' base of 140,000 members in the Los Angeles area.

"This kind of progress is far better than I expected," Georgine said recently. "I had expected a long, protracted battle . . . without this kind of immediate gain."

Georgine concedes that the campaign was buoyed by a general building boom that vastly expanded the construction job market in southern California - a boom that could go bust threatening all the unions' gains if the Carter administration's anti-inflation in and dollar-rescue efforts produce a serious economic slowdown in the near future.

But he contends that the Los Angeles effort has demonstrated sufficient potential to warrant expansion on a sustained basis, even if a recession reduces the number of jobs and intensifies competition for them.

The whole idea is to impede growth of the open shop [which is open to nonunion as well as union workers], and we've shown we can do that . . . we've accomplished that in L.A.," said Georgine.

It was during the recession of the mid-1970s that the open shop movement broke the union domination of American construction, capitalizing on a severe shortage of jobs to increase its competitive advantage over the high cost and restrictive work rules of unionized construction.

The erosion became so serious that the unions modified many of their work practices, moderated their contract settlements and, breaking with a long histroy of trying to restrict their own membership, embarke d on their first coordinated organizing drive in history.

Los Angeles was chosen in part because it was still union territory but vulnerable to open shop incursions. "They were saying, 'California, here we come'" said Georgine, and the unions were showing some signs of decline.

Whether the Los Angeles organizing drive has dealt more than a glancing blow to the open shop movement is not yet clear. Even Georgine is guarded in claiming a decisive turnaround. Coh O'Shea, special AFL-CIO representative in charge of the Los Angeles effort, sayd "there's still a helluva long way to go."

The Associated Builders and Contractors (ABC), representing largely nonunion employers, reports its membership has picked up substantially in recent months and says none of its members has been unionized.

"To that extent, their campaign has been a bust," said John L. Fielder, president of the ABC's southern California chapter.

But Fielder concedes that some workers on open shop projects may have been recruited into the unions and that "labor problems," including picketing and slow-downs by some union subcontractors, have caused delays in completion of some jobs.

O'Shea said about 5,000 of the 10,000 new union recruits formerly worked on open shop jobs. "We feel they [open shop projects] have been slowed down substantially," he said.

One of the main attractions of nonunion contractors has been their promise of on-time dependability uncomplicated by strikes and other forms of labor unrest. O'Shea said enough key workers dropped off one nonunion apartment project in Los Angeles recently that it was only half built by the time it was scheduled for completion.

What all of this may portend is increasing competition and perhaps strife - between unions and nonunion contractors over jobs once all but lost to the unions.

In the Los Angeles drive, for instance, most of the new union membership came in residential construction, principally single-family homes and smaller apartment complexes. Unions have been virtually closed out in many other areas.

Moreover, ABC is not only vigorously fighting the union drive in Los Angeles but also mapping a counter-offensive to expand its membership in metropolitan areas, hoping to raise it from 12,500 to 22,000 individual contractors by 1983.

As for the unions expanded organizing campaign, Georgine said that in addition to beefing up the Los Angeles effort, the unions have been asked to start drives in Washington, D.C., Baltimore, the Carolinas, Phoenix, Ariz., and the Erie, Pa., area. New targets will be added gradually, he said, sixth one or more to be chosen shortly.