What has surely been one of the most exciting major party nominating processes ever in Virginia has come to an end with the selection of Democrat Andrew P. Miller and Republican Richard D. Obenshain as U.S. Senate candidates.

Now, there is good reason for voters to hope that these two energetic politicians will produce an equally exciting general election contest - one in which each is forced by the other to spell out explicitly how he and his party will try to influence national policy in key areas: Taxation, management of the economy, foreign policy, defense, civil rights and the growing federal role in state and local government.

It is reasonable for voters to entertain such a hope partly because of what these candidates are not. Voters are not dealing here with charismatics. Neither has personal wealth, a famous spouse, a glittering lifestyle or a crusader's image to fog voter perceptions.

Moreover, neither of these young men - Obenshain is 42 and Miller 45 - has the political momentum of a Mills Godwin or a Harry Byrd which allows them to wear the cloak of hoary political tradition as a shield against critical injury.

What voters do have here is a couple of individuals unremarkable in every way except for their capacity to survive and speak intelligently to the issues of the time. Yet both have begun their campaigns by linking one another to polarizing figures of the recent past.

Miller has tried to saddle Obenshain with retiring Sen. William L. Scott, the controversial Republican who was elected when Obenshain was state party chairman. Obenshain has tried relentlessly to establish Miller as a supporter of former Lt. Gov. Henry E. Howell, controversial champion of the liberal faction of the Democratic party.

The fact is that Obenshain was not responsible for either the nomination or election of Scott and has almost nothing in common with that senator except a deep-seated conservatism. Obsenshain probably is willing to defend Scott's voting record, which is similar to that of the majority of the Virginia congressional delegation, but that is not likely to be Miller's point of attack.

Miller and Howell share nothing in common except a mutual low regard that, as in usual in politics, is intensified by the fact both are members of the same party. Howell beat Miller in the 1977 gubernatorial primary and supported his leading opponent for the Senate nomination.

Howell and Scott have only one thing in common. Both are now extinct as factors in statewide politics. If the two major party candidates try to revive them and the antagonisms they inspire for yet another campaign, a search for a serious write-in candidate would be the appropriate public response.

The only political figure other than the candidates who can legitimately be a factor in this Senate race is President Carter. Obenshain already has made what he perceives to be Carter's failures a central theme of his campaign.

However, if he manages to link Miller and Carter in a common political cause, he will have succeeded where Carter political aides Hamilton Jordan and Frank Moore utterly failed.

Carter's affinity for Howell set up a naturl hostility between him and Miller in 1976, and Miller, then attorney general, was a tepid campaigner for Carter in the presidential race. Carter staffers who came to Virginia from other states disliked Miller, blamed him in part of the Republican victory in the state and were delighted when Howell defeated him in the 1977 primary.

This is a history that is not likely to make Miller a defender of the President this year. In fact, the Carter issue may come down to the question of whether a member of the majority of minority party can be the most effective critic of the President in the Senate.

This is a question that Obenshain and Miller can thrash out before the voters in the debates that both sides have now promised to provide. The two candidates are able lawyers and aggressive politicians. They should be good debaters and the combat between them should not be muffled by panels of pipe-puffing journalists marshaled by the League of Women Voters or Jaycees.

These two should be allowed to slug it out, toe to toe in the classic format of argument and rebuttal that allows each to be the others inquisitor.

For the rest of us, it should be great fun.