Like eight teams of horses pulling in different directions, the local governments of the Washington area have come close to ripping apart the emergency agreement their representatives worked out nearly two months ago to continue building the regional Metro subway system.

Doubts, hostility, bureaucratic sluggishness, misunderstandings, jurisdictional jealousy and a bitter law suit have marked the course of Metro's "interim capital contributions agreement." The document is intended to pay for the completion and the remaining 40 miles is determined politically.

The plan is in limbo, holding up the award of construction contracts, the ordering of materials and the performance of work. Delays have begun adding an estimated $4.4 million a month to the $5-billion cost of the system.

The start of work on two route extensions already is being held up. One is from Four Mile Run, near National Airport, southward through Alexandria to Huntington station in Fairfax County. The other is from Grosvenor station through Rockville to the Shady Grove station in Montgomery County.

The involved history of the interim contributions agreement demonstrates the difficulty of building a transit system in two states, including four counties and three independent cities, and the District of Columbia, which are the partners in the Metro project.

Tiny Fairfax City, one of those partners, has filed suit against the agreement, contending that by, committing all available money to build 60 miles there will be no funds remaining to build the line to Vienna. That would be the only route close to Fairfax City.

Uncertainties over the impact of the law suit sent shock waves across the region.

Fairfax County and Falls Church refused, after the suit was filed to sign the agreement until the case was settled, but subsequently reversed themselves.

Prince George's concerned that the bulk of the Maryland mileage in the 60-mile system would be in Montgomery County, worried that it would be short-changed in state funds. That issue is near a resolution.

In the District of Columbia, the agreement has reached the office of Mayor Walter E. Washington for signature after being held up for a lengthy legal review in the office of the corporation counsel.

And the Alexandria City Council put off approving the measure on Jan. 25, its members saying they wanted more time to ask questions.

Ironically, the proposed regional agreement was basically the idea of one of Alexandria's own officials, Clifford H. Rusch, the deputy city manager.

Rusch was trying to figure out how to build the Metro route from National Airport through Alexandria to Huntington. The city's main concern was that the line not be terminated within the city, attracting an increased influx of Fairfax County traffic to the railhead.

Like other officials, Rusch knew that Metro was close to outstripping the roughly $3 billion available to build the rail system, and under U.S. directives the region was beginning to study possible cutbacks.

Most, but not all of the available remaining money had been committed to build the routes already under way. What could be built, Rusch wondered, if every available remaining dollar were funneled into some kind of stopgap program?

Suburban Maryland officials had similar ideas. A series of regional meetings followed to which every area jurisdiction was invited. Fairfax City, which had contributed $2 million as its full share of building a line in the Interstate Rte. 66 median to Vienna, did send representatives.

What evolved from the meetings was a plan to finance and build, to the point where train operations could begin, all the Metro mileage that was cleared for construction.

Routes blocked by political or planning obstacles were omitted. Uncertainty over the I-66 extension through Arlington was one such obstacle, which apparently was removed by the approval of the road last month by the U.S. Department of Transportation.

Under the financial plan, the local governments would contribute $125.8 million. Metro itself would provide $59 million from accumulated interest on investments. The Department of Transportation would be asked to grant enough federal aid to reach a total of $942.8 million.

This sum would be enough to build not only the Huntington and Shady Grove routes, but to complete portions of four other routes in Maryland and Virginia that already are being built. The Vienna route, as far as Glebe Road in Arlington, is one of those routes.

To carry out this program, Metro lawyers drafted the interim agreement, a relatively simple three-page document that contained black spaces for signatures by officials of every Metro governmental partner - except Fairfax City, which was not being called upon to contribute more money.

President to the Metro board Dec. 2, the document was enthusiastically endorsed. Staff officials, already realizing that some people regarded the plan as a truncation of the Metro system to 60 miles, insisted the full 100-mile system was still alive, if ailing.

At this point, the proposed agreement was "transmitted to the chief executives of the local governments" for action, according to John A. Robertie, Metro's associate general counsel. Because local officials had negotiated the pact, no further shepherding was believed necessary, Robertie said.

But different people had different perceptions.

Out at Fairfax City Hall, City Attorney John H. Rust scanned the document. Among other things, paragraph 3 caught his eye. Slightly condensed here, it read:

"No (participating government) shall be obligated to fund construction not included in this agreement or to pay in excess of the amounts specified (in it) . . . Funding of additional construction beyond that covered in this agreement shall be dependent upon the adopting of a financial plan and a new or revised capital contributions agreement."

Later, it was explained that this language was put in to comply with a state constitutional provision in Virginia that bars counties from incurring long-term debt without a public referendum.

Believing that this provision and other parts of the interim agreement effectively eliminated the Vienna line, Rust was authorized by city officials to file suit in U.S. District Court at Alexandria seeking to block the other seven Metro partners from joining a the pact.

Trial of the case took three days last week, and final arguments are expected to conclude today. Judge Oren R. Lewis is then expected to take the case under advisement.

The pendency of the law suit created additional uncertainly. Some local governments, such as Fairfax County and Alexandria, which conditionally endorsed the funding plan, drew back (although Fairfax County since has given final approval).

Throughout the region, only Arlington County approved the proposal speedily and without strings.

Across the Potomac River, a lawyer for the Prince George's County Council, like some of his counterparts elsewhere, wanted to rewrite the ambiguous Paragraph 3 to state continued support beyond 60 miles.

But his suggestion was flawed: the agreement must be signed in identical form by all seven jurisdictions or it would in fact not be an agreement.

Back at Metro headquarters, somebody suggested that the best way to clarify Paragraph 3 was to omit it entirely. Agreed. The Metro board promptly made it official. The expurgated plan was sent out to the local governments.

Fairfax County then approved. At Falls Church, an aide to the city manager, Mark Horowiz, suggested Jan. 24 that the City Council withhold approval to pressure Metro into paying more for a 6-acre tract of city-owned land slated to be part of the West Falls Church station and car-storage yard site.

The Council decided otherwise, and agreed to sign the Metro agreement, keeping the land issue separate.

Next night, the proposal was presented hastily to the Alexandria City Council, whose members balked. They voted to wait until mid-February, when they could ask more questions and, they said, get clearer answers.

Meantime, in Maryland, Prince George's officials suspected that the proposed deal would give Montgomery County a disproportionate share of funds the state has granted to support Metro construction.

That led to separate negotiations to assure future equity. The Montgomery County Council agreed. The Prince George's Council is expected to concur.

William A. Boleyn, Metro comptroller, said nothing can proceed until everybody actually signs. Even then, it would take a month or more to put the program into effect, he said.