Former Tennessee Gov. Lamar Alexander easily won the Republican nomination for Senate on Thursday, brushing aside his opponent's claims that the two-time presidential hopeful was past his political prime.

Alexander will face eight-term Rep. Bob Clement, who coasted to the Democratic nomination in the closely watched race to succeed retiring GOP Sen. Fred Thompson.

With 94 percent of precincts reporting, Alexander had 278,480 votes, or 54 percent, and conservative Rep. Ed Bryant had 221,033 or 43 percent. Five other candidates split the rest.

In the governor's race, GOP Rep. Van Hilleary and Democrat Phil Bredesen trounced their opponents to win their parties' nominations. It is Bredesen's second chance to win the job: He lost in 1994 to GOP Gov. Don Sundquist, who is barred from seeking a third term this fall.

Bredesen, a former Nashville mayor, won 79 percent of the vote in the six-way Democratic primary. On the GOP side, Hilleary had 312,993 votes, or 64 percent, while former state lawmaker Jim Henry had 147,013, or 30 percent. Four others split the rest of the vote.

Hilleary, 43, spent an enormous amount of time and energy on the campaign trail trying to link Henry to Sundquist, the current governor who was criticized after failing to oppose an income tax.

Henry, 57, a former state Republican Party chairman, countered that he was the candidate "with experience in Nashville, not Washington."

Tennessee's general election is expected to be pegged to the worsening economy -- which includes an $800 million state budget deficit. The state faced a partial government shutdown last month as the Legislature fought past the new budget year over program funding.

The state is also trying to find new sources of revenue. Hilleary is opposed to an income tax, so Democrats may approach Bredesen's November race by depicting him as a new-style Democrat who can solve the current budgetary standoff between Sundquist and the Legislature.

Thompson's retirement from the U.S. Senate prompted five Democrats and seven Republicans to try to get the nod from their respective parties.

Alexander has name recognition to help him out. Along with being a former two-term governor, he also has served as president at the University of Tennessee and as U.S. Education Secretary. He ran twice for president.

White House political chief Karl Rove had asked Bryant not to run against the better-known Alexander for the sake of party unity. But the four-term congressman who was a House manager during President Clinton's impeachment proceedings refused to clear the way for Alexander, a veteran politician many remember for walking 1,000 miles in 1978 to court voters in a plaid shirt.

Bryant, 53, launched a vigorous campaign in which he called Alexander, 62, too liberal and a politician past his prime. Alexander accused Bryant of being an ineffective lawmaker and the party's worst hope of attracting moderate voters in the general election.
Clement, 58, had little opposition in his primary and banked more than $1 million, while Alexander and Bryant spent most of their campaign funds fighting each other.

The names of both Al and Tipper Gore were floated for the Democratic nomination early after Thompson announced his retirement, but both ultimately decided against running.

About 400,00 voters, or 12 percent, of the state's 3.3 million registered voters, cast ballots during the July 12-27 early voting period.

All of the U.S. House seats are up for re-election and have numerous candidates running.

Among the crowded races for Tennessee's three open House contests, state Sen. Marsha Blackburn was expected to win the GOP nod in Bryant's solidly Republican 7th District. If she wins this fall, Blackburn would become the first woman sent to Congress from Tennessee who did not succeed a husband who died in office or while campaigning.

Thursday was also the general election for county offices.

One of the quirkier aspects of this year's campaign has been a sheriff candidate on a horse.

Trousdale County sheriff candidate James Wright, 56, saddled up his horse and hit the rural campaign train.

"I was just kind of thumbing through this book and read about this story of this guy who rode out west campaigning and thought that would be a good idea," Wright told Fox News while on the campaign trail. "Anything unusual stands out in people's minds … hopefully, they will vote accordingly."

Fox News' Liza Porteus and The Associated Press contributed to this report.