Virginia Republicans, perhaps as many as 7,000 of them, are going to gather in this city this weekend for what is expected to be the largest state political convention in the history of the nation.

For a party that was only a nuisance factor in Virginia politics a generation ago, the convention has taken on the appearance of a grand celebration of coming of age.

The object of the game is to nominate a U. S. Senate candidate for the seat being vacated by retiring Republican William L. Scott. The expected throng of delegates is largely the result of vigorous campaigns for the nomination by the three leading contenders, former Gov. Linwood Holton, former Navy Secretary John W. Warner and former national GOP cochairman Richard D. Obenshain.

State Sen. Nathan H. Miller, of Rockingham County, is running a distant fourth by all calculations, but his earnest campaign has greatly enhanced his potential as a future statewide candidate, probably for lieutenant governor or attorney general in 1981.

Despite the euphoria among state GOP leaders over the prospects of an exciting and financially profitable convention, there is some well justified apprehension over how well it will function as a nominating process.

Virginia is the only state in the nation in which the major parties are authorized to nominate their Senate candidates by convention this year, and both Virginia parties have chosen that route. State Democrats, weary of divisive and expensive primaries, will hold their nominating convention in Williamsburg June 9 and 10.

To bolster confidence in the parties and in the state's electoral process as a whole, it is important that both Republicans and Democrats hold efficient meetings and produce nominees that everyone believes were chosen fairly.

One of the concerns about the Republican convention is that the unusually large number of delegates will result in confusion and tedious roll calls. Convention rules permit each city and county to send as many as five delegates for each vote.

One high-ranking Republican worried privately last week that "we are bringing a lot of new people into the process this year, but if the convention goes badly we may turn them off for good."

The convention planners hope they have assured smooth roll calls - there could be three or more to choose a nominee - with a system of roll call captains assigned to each 100 delegates. The goal is to complete each convention vote within one hour.

Republican hopes for a smooth convention also rest on the belief that serious rules and credentials fights will be avoided. The Democrats, on the other hand, are geared up for an enormous rules battle with front runner Andrew P. Miller on one side and the seven trailing candidates on the other.

Republican front runner Obenshain defused a potential GOP convention controversy last week by releasing more than 300 Richmond area votes, almost 10 percent of the 3,081 convention votes, from city and county instructions that bound them all to vote for him.

Instructed delegations - those bound by a majority vote of a city or county mass meeting to vote for one candidate even if some delegates prefer another - are deeply resented in many parts of the state. There is a good chance Obenshain would have lost a floor vote over the right to have instructed delegations. By releasing them, by probably lost no more than two dozen delegates and avoided a rules defeat that could have stopped his momentum at the convention.

One question party leaders will have to resolve shortly after the convention is what to do with an expected profit of about $75,000 the party will reap, primarily from delegate registration fees.

The Republicans have run an ambitious state operation under Chairman George N. NcMath, but the party's affluence has been more apparent than real. Despite record fund drives, the party has $100,000 in debts accumulated during 1976 and 1977. Spending this year has been held within receipts.

There will be a great temptation to use a large part of the convention profit to reduce the debt.However, the party leaders have a moral obligation to see that the GOP nominee benefits from the convention by getting the maximum amount of state party aid that is allowed by federal law in the general election.

The federal formula should permit a party contribution of about $85,000 this year. The $15 delegate registration fees that will be paid by the rank and file Republicans attending the convention will make such a contribution possible. It would greatly enhance the stature of the convention process if the registration money actually flows through the Republican campaign next fall.