The war for the Republican presidential nomination -- and for the soul of the Virginia Republican Party -- passed quietly through Alexandria yesterday: no back-stabbing, no smoke-filled rooms, not even a nasty word.

Alexandria became the second Virginia locality to choose delegates in the lengthy process of picking the GOP presidential nominee. An estimated 1,500 voters turned out at the School Administration Building to select 59 local delegates to the state convention June 10, when Virginia's 50 representatives to the Republican National Convention will be selected.

There was little sign of the hostility brewing between Virginia native Pat Robertson, whose campaign is built largely on Christian newcomers to the GOP, and the traditional Republican establishment.

It was impossible yesterday to tell exactly who won in Alexandria because of the GOP's complex balloting system. The votes will take days to count, and even then the results will be uncertain because voters chose state delegates, not presidential candidates. Also, the delegates are free to change their allegiance before the state convention in Roanoke.

Supporters of all four Republican presidential candidates -- Robertson, Vice President Bush, Sen. Robert J. Dole of Kansas and Rep. Jack Kemp of New York -- agree that each got a healthy share of the city's 59 delegates to the state convention.

The business of selecting the more than 3,000 state Republican delegates will be conducted in a series of local caucuses and conventions that began in Newport News and will climax at the state convention. Fairfax County will hold local voting on April 13 and a county convention on April 30.

However, campaign officials and Alexandria party leaders agree that the candidates' order of finish may not have been the crucial aspect of yesterday's voting in the city. The real victory, they say, was avoiding a bloodbath like the one in Newport News, where the party's first presidential voting took place a week ago.

There, Robertson forces elected one of their own as city chairman and swept 90 of the city's 96 delegates to the state convention. A prominent Newport News City Council member, angered by the Robertson takeover, renounced his Republican affiliation. And deposed party leaders showed up at a unity dinner wearing black armbands.

The key to the struggle within the Virginia GOP -- and to which of the presidential candidates will win Virginia's 50 delegates to the national convention -- is the party's complex nominating process. Political activists say the process gives a decided edge to Robertson, whose supporters are dedicated and disciplined, and to Bush, who appears to have the broadest backing among traditional party activists.

Unlike Virginia Democrats, Republicans are putting little emphasis on the state's "Super Tuesday" primary election March 8. For Democrats, the primary will determine how many delegates go to each candidate. But for Republicans, the primary is a nonbinding "beauty contest."

The GOP caucus system, which the party has been using for decades, is itself the focus of considerable controversy. Its intricate rules, which vary widely from place to place, and elaborate protocol are a mystery to all but a few party activists.

Even the Virginia political operatives for Robertson, Bush and Dole call the system exhausting and sometimes maddening. "It's scary and it's intimidating to people," said Ann Kincaid, Robertson's state coordinator. Added M. Boyd Marcus Jr., a prominent Bush supporter, "You can't explain it. All you can do is grossly oversimplify it."

But to win in Virginia, every Republican candidate must unravel the complexities of the caucus process. The voting in Alexandria was an instructive, if typically convoluted, example of how the system works.

First, Alexandria Republicans are different from those in many other Virginia localities because they allow voters to make their selections by secret ballot. Under city rules, any registered voter who signed a written promise to support the Republican nominee in November was allowed to vote.

Caucuses require all participants to remain in a meeting for several hours and to cast their votes in public, usually by raising their hands. Alexandria has traditionally used a canvass because it is faster and less confusing than a caucus.

But even canvasses can be complicated. The ballot that was handed to Alexandria voters yesterday was far more complex than a general election ballot. It did not include the names of all the presidential candidates. Instead, it included the names of more than 300 people who were running to become delegates to the 8th District Republican convention in May and the state convention in June.

In reality, there was not much of a contest. Each of the presidential candidates had rounded up supporters to run as delegates, but no one was able to get a clear majority. Therefore, campaign officials decided before yesterday's voting to forgo a head-on battle and allow each candidate a share of the delegates.

Even after the delegates are elected, the candidates will have to turn out their supporters for both conventions this spring. The candidates also must continue courting their delegates, because under party rules many are free to change their minds about whom they support.

As the process drags on, the dedication of Robertson's supporters and the political experience of Bush's backers are expected to pay off. "We're in this for one reason, and that's to elect Pat Robertson," Kincaid said. "This is his home state, and we want to go all the way with him."