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(CNN) — Voters in Kentucky and New York are going to the polls Tuesday in primaries that were delayed by the coronavirus pandemic and are being conducted largely by mail.

With hours of voting remaining, the disastrous primary days that have occurred in other states, including Wisconsin, where lines stretched for several blocks throughout Milwaukee, and Georgia and Nevada, where voters waited in line for hours, did not seem to be materializing on Tuesday.

“So far, this has been a very successful election,” Kentucky Republican secretary of state Michael Adams said at a state Board of Elections meeting Tuesday. “Things are going great. Voters are really happy. I think they’re a little relieved that this process has been so easy for them today, that we’re getting a big thumbs up given the dire predictions over the weekend.”

As the state grappled with massive shortages of poll workers, Kentucky’s two largest cities each consolidated down to one massive polling place — the Kentucky Convention Center in Louisville and the University of Kentucky football team’s Kroger Field in Lexington.

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By midday, lines in Lexington stretched for about an hour, according to local media reports and voters who posted about their wait times on social media. Adams said he expected those wait times to resolve by the afternoon.

In New York, meanwhile, early reports emerged of some voters being handed the wrong ballots or incomplete versions of their ballots.

In Kentucky, Democratic voters are deciding a closely watched Senate primary between Amy McGrath, a former fighter pilot who is backed by the national party establishment, and Charles Booker, a Black state lawmaker who has emerged as a national voice in recent weeks during protests over police brutality and racial injustice. The winner will take on Senate Majority Leader Mitch McConnell in the fall.

In New York, several competitive House primaries are at stake — including progressive Jamaal Bowman’s bid to unseat longtime Democratic Rep. Eliot Engel.

Kentucky’s consolidation from 3,700 polling places to less than 200, including just one in the state’s two largest cities, led to concerns of a suppressed Black vote, including from national figures such as Hillary Clinton, NBA star LeBron James and Stacey Abrams, the former Georgia gubernatorial candidate.

Booker has also been a vocal critic of the state’s limited in-person voting options. His campaign organized free Lyft rides to the polls.

Democratic Gov. Andy Beshear and Republican secretary of state Adams have repeatedly pointed out that the state allowed everyone to vote by mail after it delayed its March primary due to the coronavirus pandemic.

“They misrepresented what a Democratic governor and I put into place,” Adams told CNN of the concerns and criticism.

“We spent several weeks negotiating. I got some things I wanted; he got some things he wanted. It was a good outcome for voters of both parties and Republicans and Democrats both have responded positively to the more options to vote,” he said.

Results in both states will likely be delayed due to an increase in mail-in voting.