Fairfax County's inadequate and heavily traveled secondary roads need an estimated $350 million worth of improvements, but the new state highway budget contains less than $40 million for such work over the next six years.

Fairfax Supervisor Joseph Alexander (D-Lee), complaining that "we're not even using a Band-Aid approach," says it's time to go to the county taxpayers for bond money to pay for "critical projects."

Although the county has used bonds to pay for schools, libraries, parks and mass transit, it has never done so for roads. Instead it has relied almost wholly on state funds, with a small fraction coming from federal revenue sharing.

"I don't see any other way than bonds," said Alexander, who discovered that some badly deteriorated roads in his Lee District were not scheduled for repairs in the Department of Highways and Transportation's six-year construction plan. Alexander said he would like to see a $20 million bond issue for roads put before the voters as soon as next year.

Coming as it did in an election year, Alexander's proposal generated little spontaneous sympathy from his colleagues on the Board of Supervisors.

"That's the first time I've seen the board without anything to say," said Donald Keith, who heads the Fairfax office of the Virginia Department of Highways and Transporation.

Supervisor Marie Travesky (R), whose Springfield district probably has the least adequate roads, said after the budget meeting: "I think a bond issue would be extremely unpopular. I would like to see us go for taking over the road system."

Travesky's district has many roads that were designed when their traffic was oxen taking hogsheads of tobacco to market or horse-drawn wagons carrying hay. Today those roads, modernized with a layer of asphalt but just as narrow, winding, high-crowned and shoulders-less, each carry thousands of cars during rush hours and other times of the day.

One road, Hooes, was so badly deteriorated last year, that fire trucks would not travel on part of it.

Board chairman John F. Herrity (R), who represented Springfield from 1972 to 1976, said, "I think a bond issue is something that needs to be looked at," but wouldn't commit himself one way or another. He added, though: "Bonds have to be considered in the context of all our capital needs. We can't do everything for everybody."

In 1971, the highway department spent 56 cents of every dollar on new construction. This year it is spending only 51 cents. Maintenance took 18 cents in 1971, but in 1979, because of inflation, it requires 25 cents.

"We're getting further and further behind [on improvements]," Keith said, noting that the state tax on gasoline [the major source of funding] has stayed at 7 cents a gallon while the growth of revenues has been checked by the appearance of more high-mile-age cars.

Most localities in the state complain they need more road money than they get, but Fairfax's problems are aggravated by its rapid growth - most of it in areas that are served by roads built for an earlier, rural population.

The county's master plan permits medium and even high densities (up to eight dwelling units an acre) in many unsettled areas. The plan does not tie such densities to road improvements. The county gave up trying to do that after it lost two major rezoning cases, where judges ruled that services followed the population.

A bond issue for roads would almost certainly have to displace one or more other major services. The county already plans to go to the voters between now and 1984 for $181.4 million worth of bonds for schools, parks, libraries, fire and rescue services, storm drainage and Metro rail. Schools are the biggest item, but growth in the southwestern and northern parts of the county have made education perhaps the highest priority.

Another big bond issue - $40.8 million - would involve Metro. But unless that is approved, Fairfax would probably not get any significant rail service.

Without rail service, the already overburdened roads will get even worse.