Republicans and Democrats will vote on candidates for lieutenant governor, labor commissioner and corporation commissioner.
Republicans will also be voting on candidates for auditor and inspector, attorney general, state school superintendent and insurance commissioner.
All five U.S. House districts have primaries on Tuesday, with the two in eastern Oklahoma drawing the most interest.
In the 1st Congressional District, in the Tulsa area, Democratic and Republican primaries are crowded with candidates hoping to replace Jim Bridenstine, a Republican who resigned this year to take the helm at NASA.
In the 2nd Congressional District, which includes most of eastern Oklahoma, Rep. Markwayne Mullin, R-Westville, is running for a fourth term, after pledging in 2012 to serve only three terms. Mullin has three opponents. Four Democrats are vying for the nomination in the district.
U.S. Reps. Tom Cole, R-Moore, in the 4th Congressional District; and Steve Russell, R-Choctaw, in the 5th Congressional District, also face primary opponents. U.S. Rep. Frank Lucas, R-Cheyenne, does not have a primary in the 3rd Congressional District.
Primaries will be held in nearly three quarters of the 101 state House districts, with 32 sitting members facing challenges in their parties. There are 20 Senate primaries, with six incumbents facing opposition.
Oklahoma saw a surge in candidates this year, as nearly 800 people registered to run for office, the most of any year since 2000, the last year for which the election board has records. Slightly more than half of those registering this year did so to run in legislative races.