When forming the New Summit County Republicans, the group challenging Alex Arshinkoff's 30-year hold on the chairmanship of the county Republican Party, Kevin Coughlin outlined an orderly campaign.

The state senator from Cuyahoga Falls and his allies would define Arshinkoff's negatives. They would recruit candidates to run for the Summit County Republican Party Central Committee in the March 4 primary, gaining a power base from which to elect a new chairman.

They would announce their candidate, eventually winning with a combination of newly elected Central Committee members and converts.

If orderly enough, the process did surprise this week. In the bright, airy lobby of the John S. Knight Center, the person widely rumored to be the leading candidate to oust Arshinkoff, trial attorney Don Varian, took to the podium to denounce a local party ''in disarray.'' But just at the point where everyone expected Varian to say, ''and that's why I'm running,'' he turned the microphone over to Carol Klinger.

The 14-year member of the Cuyahoga Falls City Council and Goodyear manager (with a background in accounting and an MBA in finance) is little known outside her home territory. She has run once countywide, for auditor.

In brief remarks to an audience of about 35, Klinger promised a back-to-the-basics approach, with tighter controls on party spending and more attention to grass-roots organization and candidate recruitment. Coughlin, it turned out, was on a family vacation in Washington, D.C.

After the March 4 election results are certified, probably by the middle of next month, the Central Committee will meet and decide how to elect a new chairman.

Between now and then, Arshinkoff and his allies and Klinger and her allies will direct their efforts at the 475 precinct-level representatives on the Central Committee. Nobody else matters.

It's tempting to dismiss the whole thing as something akin to a battle for control of the English Department at your local state university. The ferocity of the fighting is inversely proportional to what's really at stake.

It was Varian (who almost challenged Arshinkoff three decades ago) who raised the larger issue, the importance of having a viable, broad-based Republican Party capable of contributing in a positive way to the direction of the city and county.

The Akron City Council is now totally dominated by Democrats; the Summit County Council is down to a single Republican, Louise Heydorn of Silver Lake, who was taken out in the primary by state Rep. John Widowfield, a Cuyahoga Falls Republican and Arshinkoff ally.

Akron is indeed a tougher nut to crack for Republicans than it used to be. Changing demographics and some of the lowest campaign finance limits in the country have created a difficult environment for challengers of either party. But county government is not as difficult, with no fund-raising limitations and blocs of suburban voters who, like Klinger, are drawn from the professional, technical and managerial ranks and who can be persuaded to vote Republican if presented with the right candidate and the right message.

Varian admitted that the effort to win a majority on the Central Committee for Klinger will be a difficult process. He did promise that the struggle for control of the local Republican Party won't end if Klinger doesn't make it, stressing that the ''movement'' is much broader.

The irony at this point is that the New Summit Republicans have already made a mark of sorts, influencing Arshinkoff, also a paid lobbyist who operates in Columbus and Washington, D.C., to pay close attention to the grass roots, starting with the precinct-level representatives who put him into power in the first place.

Local candidates running last fall also received the support and attention of the Summit County Republican organization, although a trio of high-profile, Arshinkoff-backed candidates (Widowfield in the clerk of courts race in Cuyahoga Falls, Diana Stevenson in the race for municipal court judge in Barberton and Brian Daley in a Hudson City Council contest) all lost.

Grass-works work is exactly what Arshinkoff doggedly pursued when he first became chairman, at a time when the Republican Party was at a low ebb.

By the mid-1990s, with the tide turning in the GOP's favor, the groundwork paid off, with Republicans battling to near parity with Democrats on the ballot in Summit County. That's slipped somewhat, with a recent tally showing the GOP's percentage of officeholders down to around 39 percent.

With the tide in Ohio turning in the Democrats' favor, Arshinkoff may once again be entering a rebuilding phase, his attention focused on local races and candidates, precisely where Klinger argues it should be.

In the current political climate, Arshinkoff can ill afford a continuing battle over leadership of the party. This time around, the Summit County Republican Party Finance Committee pledged to raise $350,000 to support Arshinkoff's battle to retain the chairmanship, a battle he appears to be winning. But as King Pyrrhus of Epirus remarked after a costly victory against the Roman army, ''Another such victory over the Romans and we are undone.''