Ashford was running to reclaim the seat he once held but lost in 2016 to Republican Rep. Don Bacon.
Buehler, who ran for secretary of state in 2012, was the most centrist of the Republican front-runners.
In 2015, Ashford upset eight-term Republican Congressman Lee Terry, and served one two-year term, only to then be defeated by Bacon with a margin of less than 4,000 votes.
Ashford had the backing of national Democratic leaders, including his former colleagues in Congress who donated to his campaign.
Democrats Vanessa Gayle Ward, an Omaha community activist, and University of Nebraska at Omaha instructor Tyler Davis were also seeking the nomination in their first bids for public office. She ran unsuccessfully for lieutenant governor in 2014 as part of Democrat Chuck Hassebrook's gubernatorial campaign.
Raybould defeated three Democratic challengers in Tuesday's primary race for the seat held by Republican Sen.
In the GOP primary, Fischer defeated retired Omaha math professor Jack Heidel; writer and retired air conditioning technician Dennis Frank Macek; former finance manager Jeffrey Lynn Stein; and Lincoln businessman Todd Watson.
The other Democrats were Frank Svoboda, a retired farmer, attorney and judge from Lincoln; Larry Marvin, a retired real estate broker from Fremont; and Chris Janicek, of Omaha, who owns a specialty cake business.
Key primaries in Nebraska's congressional districts remained too close to call at 10 p.m. Tuesday.
Knute Buehler has won the GOP gubernatorial primary, besting a crowded field vying to compete against incumbent Democrat Kate Brown in November.
Nebraska state Sen. John Murante won the Republican nomination for state treasurer and is all but certain to get the job in November.
The polls have closed in a Nebraska primary election that will set up races for U.S. Senate, governor and the U.S. House.