Virginia Republicans asserted their growing strength in Tuesday's elections -- especially in some former Democratic strongholds in Northern Virginia -- but failed to make any dramatic gains in the legislature.

The most striking GOP victories came in Fairfax County where Republicans captured eight of 10 House of Delegates seats and ran well in other local and legislative races.

"There's nothing the Republican Party can't do here now," gloated Nicholas Panuzio, the county's GOP chairman. "I'm just sorry we didn't run anyone for Commonwealth's Attorney."

In addition to providing the party with two of only three new GOP seats in the House, Fairfax Republicans narrowed the Democratic majority on the board of Superviors and came within 1,000 votes of ousting an incumbent state senator.

"I'm really delighted I've survived," said Del. Gladys Keating, one of only two Democrats to win House seats in Fairfax.

The GOP also picked up three seats in the state Senate, giving the party 9 to 40 senators and 25 of 100 House of delegates seats. Those were larger proportions than the Republicans had ever won before but nowhere near enough to challenge the Democrats' traditional hold on the General Assembly. eNor will it give Republican Gov. John N. Dalton the comfort of a certain bloc that can sustain his vetoes.

Still Dalton, who campaigned heavily for GOP candidates throughout the state, claimed victory.

"In the end, the only sound analysis of the election is this: we went up and they went down," Dalton told a press conference in Richmond yesterday.

"The only area for debate is just how big was the Republican victory."

State GOP chairman Alfred Cramer acknowledged he was somewhat disappointed in his party's showing and his Democratic counterpart, Richard j. Davis, branded the Republican effort a failure.

"Gov. John Dalton's goal of a veto-proof legislature missed by a wide margin," said Davis. "For that reason, we consider the election a major success."

GOP strategists had targeted nine Democratic-held state Senate seats.

The Republicans took three of those seats, knocking off three veteran Democrats and electing the state's first women senator, Eva F. Scott, in rural Southside Virginia.

In Northern Virginia, the GOP had hoped to defeat, Democratic Sens. Joseph V. Garland Jr. and Charles L. Waddell, as well as seize the seat vacated by retiring Sen. Omer L. Hirt. They failed in all three attempts, coming closet in Waddell race in which Republican Thomas D. Rust outspent Waddell by nearly 5 to 1 and came within 1,000 votes of victory.

In Alexandria, voters continued the partisan split in the city's House delegration by electing Republican David Speck and Democrat Bernard F. Cohen to two House seats vacated by incumbents from both parties.

Unlike the election two years ago, Speck's victory came without the support of any special interest groups. The only other Republican to win a House seat in the city this century did so in 1977 by ousting a powerful incumbent Democrat who opposed the Equal Rights Amendment.

Northern Virginia's 27-member delegation in Richmond this January will include 17 Democrats and 10 Republicans, an increase of three GOP legislators compared to last year's session. But veteran Assembly members said they expected the delegation to function as a cohesive unit on regional legislation.

"All those elected didn't have any big differences in this campaign so I don't see a whole lot of change as far as the delegation is concerned," said Del. Vincent F. Callahan Jr. (R-Fairfax).

The majority of the region's Democrats and Republicans support Metro and will be cooperating in efforts to fund the subway system, he said.

One of the most outspoken foes of proposals for financing Metro, Del. Robert l. Thoburn, lost his reelection bid in Fairfax County. Thoburn was the only incumbent Republican legislator in the state to be defeated, but he will be replaced in that House seat by another GOP conservative, Lawrence D. Pratt.

Callahan said that the 4-to-1 Republican majority in each of the county's two House districts represent the most "lopsided split" ever in flavor of the Republicans.

Only when Republican Gov. Linwood Holton was elected to 1969, did the GOP manage to elect more candidates to the House from Fairfax than the Democrats did, Callahan said.

Dalton and other Republicans said yesterday that the party had finally over come fallout from the Watergate scandal.

Statewide, the election results are expected to have little impact on next year's General Assembly session.

State Sen. Adelard L. BRAULT (D-Fairfax), 70, who won a bitter political battle with GOP challenger John M. Thoburn, 22, son of the defeated Fairfax delegate, had threatened "repercussions" against Dalton, who had campaigned for Thoburn.

But others said yesterday they thought it unlikely that the Democrats -- who are largely split into liberal and conservative legislative factions -- could agree on an alternative to whatever legislative program the governor proposes in January.

Strategists from both parties said they were uncertain how Tuesday's results would affect next year's presidential race or the 1981 gubernatorial election.

One of 1981s likely candidates, Democratic Lt. Gov. Charles S. Robb, of Mclean, said the results did not discourage him from considering the govern's race. "It seems to me that there was no conclusive trend either way." said Robb.

Whateverithe eventual impact on future races in the state or region, however, Tuesday's results appeared to have taken their toll on local party workers.

At Fairfax County Republican head quarters, for example, a woman answered the telephone yesterday on the second ring. There was no answer at Democratic headquarters.