Construction has begun on a second section of 1-66 between Capital Beltway and the Potomac River, with work on a tleast two more sections scheduled to begin early next year, according to the Virginia Department of Highways and Transportation.

The work continues despite a pending a court suit against state of Virginia, brought by civic groups that have been fighting 1-66 for more than a decade. This summer, the U.S. Court of Appeals in Richmond agreed to consider a permanent injunction that would prohibit completion of the road, but allowed construction to begin. The court heard arguments in the case Oct. 4 but ha yet to hand down its decision.

Hank Levine, attorney for the Arlington Coalition on Transportation (ACT) and other civic groups still tilting against 1-66, said this week the issue may be moot where bulldozers already have cut down all the trees. "But there's a lot of woods still in its natural state and now we're just all sittting around holding our breaths."

A major two-mile section of 1-66 - between Rte. 7 and the Arlington County line - also would be under construction now but is being held up by the wage dispute between Virginia and the U.S. Department of Labor.

The entire 9.6 miles of 1-66 between the Beltway and Theodore Roosevelt Bridge over the Potomac now is scheduled for completion in 1981, assuming Virginia wins its final day in court, highway design engineer W.J. Butler said this week.

The latest construction to get under way is a one-mile section on the Arlington-Fairfax County line, around the intersections of Lee Highway, Washington Boulevard, Westmoreland Boulevard and Fairfax Drive. The contract cost of the one-mile segment is $13 million and involves several bridges, rebuilding roads and constructing numeroud retaining and sound-deadening walls.

The 20-year controversy over compelting 1-66 inside the Beltway appeared to be over last August when trees were razed and bulldozers began clearing a 1.4-mile section between the Beltway and Rte. 7. That segment, with a contract cost of $9.6 million, is now larged cleared.

In the wage dispute holding up work between Rte. 7 and the Arlington County line, the Labor Department contends that construction workers on the section must be paid at a "heavy construction" rate, which is almost twice what workers are being paid for "highway" construction on the two 1-66 projects already underway.

Labor officials have contended that construction of Metrorail in the 1-66 median makes this section a "heavy construction" project. Butler says a meeting to resolve the dispute, which began last summer, will be held early next year.

While the 9.6 mile segment of 1-66 is to be a no-truck, four-lane, landscaped "parkway" similar to the scenic George Washington Memorial Parkway, bulldozers so far have ebben cutting and clearing virtually at trees along the highway right of way. Butler said this week "there are going to be a great many trees eliminated along 1-666 but we're trying to save everything we can . . . and we're going to landscape it and plant a lot more trees, and larger trees, than we have along other highways. We're going to screen just about everything. We're going to do our best."

Construction on two additional sections of 1-66 will be advertised for bids shortly, one between Glebe and Kirkwood Roads - where 1-66 will again cross Lee Highway near Spout Run - and the second between Sycamore and Harrison Streets. The Rosslyn section of 1-66, which will enter Rosslyn at the western end of Key Bridge, will be the last segment to be completed, Butler said.