A. Joe Canada, candidate for the Republican nomination for lieutenant governor of Virginia, stood amid revelers at a black tie, GOP fund-raiser in Arlington recently and told a reporter how he won over the clientele of a Suffolk truck stop by arm wrestling every driver there.

For the rugged state senator from Virginia Beach, it was a display of his rapport with working people. He regards it as testimony to his electibility and therefore another reason for the Republican state convention to nominate him on June 4 instead of former state secretary of finanve Walter W. Craigie Jr.

Craigie is a Richmond investment banker and not at all the sort of person you would expect to find arm wrestling in a Suffolk truck stop.

However, in another corner ofthe Army-Navy Country Club ballroom, he gamely bared his own identification with populism, which he said is rooted in thetraditions of his self-made father, a leading Virginia municipal bond counselor.

"Because of his family situation, my father went to work at 14," Craigie said. "When the Depression hit, he had to build his business all over again, and I have learned from him."

Then, as if to erase any doubts about the depth of his working tradition, Craigie said, "I sold my first municipal bond when I was only 11 and working on Saturdays in Dad's office."

Asked in jest if he will run as a populist, Craigie answered, "Well, I am a populist. I will have appeal to black voters, to working people, to Jewish voters. For instance, the B'nai B'rith, the Anti-Defamation League - I've been going to their banquets for years."

When the Republicans gather in Roanoke to nominate their candidates for governor, lieutenant governor and attorney general, Canada's arm wrestling prowes and Caigie's banquet attendance record are not likely to be explicit issues - but electibility will.

Ten days after the June 4 Republican balloting, Democrats will hold a Virginia primary to nominate three candidates for statewide office that many Republicans fear will pose a severe threat to their party's recent domination of statewide elections.

More than anything, Republicans fear that a gubernatorial primary victory by former Attorney General Andrew P. Miller will lead to a return of the moderate-conservative Democratic coalition that reduced the Virginia Republican Party to a nuisance factor in the years before 1969. That was the year Linwood Holton became the first Republican governor in this century.

Lt. Gov. John N. Dalton is unopposed for the Republican nomination for governor. He is expected to mount a well organized and well financed campaign in the fall, but clearly faces a tough race against either Miller or former Lt. Gov. Henry E. Howell.

With their gubernatorial nomination decided by default, the Republican can devote themselves in Roanoke to the Craigie-Canada contest and the race between Del Wyatt B. Durrette Jr. (Fairfax) and Sen. J. Marshall Coleman (Staunton) for attorney general.

The Coleman-Durrette duel has dominated the delegate selection process that ended Friday after two months of mass meetings of Republicans in every city and county in the state.

Party leaders see both of the attorney general candidates as able campaigners who are more likely than either Canada or Craigie to one day head a Republican ticket as candidate for governor.

Moreover, both are now considered to have an excellent chance of defeating any one of the four Democratic candidates for attorney general, none of whom went into the primary campaign with a statewide following.

About 3,000 delegates have been selected at mass meetings to cast about 1,000 votes of Roanoke. Exact counts may not be known until roll call day because some small cities and counties may not send any delegates, and thus lose their votes, and many delegates who qualified may not show up.

Uncertainly over who will vote is one factor contributing to doubt about the outcome of both cotested nominations. party officials and candidates said in recent interviews that both races are close and expect neither to be clearly decided before the roll is called in the Roanoke Convention Center.

The wooing of delegates has been bereft of debates on policy issues. The small Republican Party is clearly identified in most minds as consistently conservative in its devotion to limited government. The limited union of Republicans and conservative Democrats in Virginia since 1969 has some how served to soften the progressive thrusts GOP leaders and legislators once made at the government establishment.

The possibilities for sharp diagreements among candidates over how to change the course of the government is further limited by the fact that former Democrat Mills E. Godwin now serves as the Republican shief executive.

Godwin is firmly pledged to campaign for Dalton ad no candidate for the secondary spots on the ticket has come close to treading on Godwin's sensibilities with proposals that appear to criticize things as they are.

Coleman is credited by party officials with making the attorney general contest the dominant race by waging a vigorous campaign as an underdog to Durrette, who began far ahead on the strength of apparent backing by party conservatives.

"I get the impression that Coleman can make three times as many phone calls in a day as any other person alive," a neutral campaign official said in an interview. "He has simply gotten in there and made a race of it."

Durrette began the race with expectations for huge delegates margins in the Eighth and 10th Congressional Districts in Northern Virginia and in the conservative Third District, which includes Richmond and its suburbs in Henrico and Chesterfield County.

He appears to have held his Northern Virginia strength, but Coleman has made deep inroads in the Third and claims he will win there on the strength of margins in the two counties.

Coleman also has had success in the cities of the Hampton Roads area. Last week, he claimed to have won 62 of 63 votes in Virginia Beach.

The Craigie-Canada contest has partly turned on the question of ticket making by Godwin and Dalton. Canada was until April, the only Republican candidate for Helement governor. Then Craigie entered the race with the apparent blessing of Godwin, Dalton and party conservatives who are close to both.

Canada refuses to acknowledge that either Godwin or Dalton favors Craigie, but he did say last week. "It is a question of whether a few powerful men or ordinary people will nominate our candidates."

Dalton officially has declared he will be pleased to run with either candidate, but the perception that he favors Craigie is pervasive.

"I think when it comes to the vote for lietenant governor," a principal convention figure said last week, "the word will go around the floor that a vote against Craigie would look like a rebuff of Dalton immediately after his nomination for governor."