During his first week as Virgina's governor, John Dalton finds himself faced with the need to decide how he will deal with federal efforts to force full desegregation of the state's colleges.

It not only is his first test, but the one by which many commentators are likely to measure the success of his entire term. Moreover, because it comes so early in his administration, it is likely to shape his relationship with his top advisers, not only those who have full-time jobs in the governor's office but those outside the government who expected the new executive to heed their counsel.

Simply put, there is a war among these advisers for Dalton's ear on the desegregation issue.

On the side of full-scale resistance to anything that smacks of enrollment quotas or federal contril of college programs are influential and conservative Democrats and former Democrats who have given Republican Dalton their support or, at least, their good will as a result of the idelogical split in the Democratic party.

These include former Gov. Mills E. Godwin, former Del. W. Roy Smith of Petersburg (now a member of the state council of higher education), state Sen. Frederick T. Gray of Chesterfield County and Robert McIlwaine, who is serving Dalton, as he did Godwin, as governor's counsel and is the link between the two administrations.

On the other side are moderate Republicans whose influence primarily comes from their close association with Dalton. They include state Sen. Wiley F. Mitchell Jr. of Alexandria, Del. A R. (Pete) Giesen of Staunton, former Gov. Linwood Holton and William A. Royall, who was Dalton's campaign manager and now is a top aide in the governor's office.

To put things simply once more, the Godwin camp has drawn a lone in the dust and dared the Department of Health, Education and Welfare to step across it by trying to impose minority enrollment "goals" on predominantly white colleges.

These men are veterans of losing battles with federal establishment over public school segregation and they see a chance to win one for a change on the issue of quotas. For them, a chance to beat the federal government in a civil rights case is reason enough to go court.

The Republican camp in Dalton's gubernatorial suite, on the other hand, wants no part of drawing any lines over a desegregation issue.

They are aghast at the prospect of beginning this Republican administration with a confrontation over a racial issue that revives memories and rhetoric from the days of massive resistance to school desegregation.

Furthermore, they firmly believe a desegregation plan can be written and carried out in a way that satisfies HEW and the federal courts without adopting quotas or permitting federal intrusion in the administration of state colleges.

There are two factors in the desegregation case that will make a settlement with HEW difficult. One is HEW's need to come up with an agreement that satisfies U.S. District Court Judge John Pratt in Washington. HEW once accepted Virginia's desegreation plans and now is acting because Pratt agreed with complaints of black plaintiffs, supported by the NAACP Legal Defense Fund, that they are insufficient.

The other troublesome factor is the lobby of black Virginians who want to preserve the racial identity of the two predominantly black state colleges, Virginia State in Petersburg and Norfolk State in Norfolk.

Black students comprise about 17 per cent of the state's college enrollment - a figure very close to the black percentage of the total population - but two thirds of the black students attend Norfolk State and Virginia State.

It is difficult to imagine how a thorough desegregation of the college system can be achieved without eventually placing blacks in a minority role at what they now regards as "their" schools.

For many black Virginians, an increase in black enrollments at William and Mary, the University of Virginia and Virginia Tech from 2 to 4 per cent to 15 per cent will be small compensation for the lost black dominance of two colleges.

So Dalton faces an authentic test of leadership. To avoid a protracted and polarizing civil rights dispute with the federal government, he may run the risk of alienating not only the conservative political establisment, whose support he has inherited, but also the black political establishment, whose support he still would like to attract to the Virginia Republican Party.

Just before he took office Saturday, Dalton rather tardily drew State Attorney General J. Marshall Coleman into the administration discussions of the HEW case. Coleman, like Mitchell, Royall and the other Republicans close to Dalton is undoubtedly counseling the governor to search for any settlement, short of abandonment of principle, that will defuse racial controversy and avoid litigation.

His views deserve to be weighed heavily by Dalton, not only because the attorney general Coleman in 1977, like Holton in 1969, proved that Virginia Republicans can compete for the state's black vote.

Whatever course Dalton takes, it is certain to be regarded as Virginia GOP policy. It is the first opportunity, welcome or not, for a Virginia Republican leader to deal decisively with a major racial issue that has matured to full term. It will be fair to judge not only Dalton but also his party on the basis of the final outcome of the college case.