Delaware permits two parties to jointly nominate the same candidate. Major parties nominate by primary, and qualified minor parties nominate by convention.
Two Libertarians, who have already been nominated by their own party, recently also cross-filed in major party primaries. Their applications were initially accepted by the State Election Commission, but now the major parties have persuaded the Election Commission to reject the filings in the major party primaries. UPDATE: on July 15, one of the candidates, Will McVay, filed a lawsuit in state court to overturn the decision. It is McVay v Dept. of Elections, Kent County, 5638-VCN.
The two candidates are Will McVay, for State House, 32nd district, and Brent Wangen, for U.S. House. Delaware has very high filing fees for candidates in major party primaries, although there are no filing fees for candidates nominated in minor party conventions. McVay paid the $834 to file in the Democratic primary, and another $834 to file in the Republican primary. Wangen only filed in the Republican primary, which cost him a fee of $3,400.
Nothing in the Delaware election law gives a major party the authority to reject a candidate who files in its primary, if the candidate meets the constitutional qualifications to hold the office and pays the fee. A 1994 Attorney General Opinion says that it is legal for someone to file in a primary if that person is not a registered member of the party. But the Opinion also suggests that such a candidate can be rejected by the major party, but there is no statutory basis.
In 2008, the Delaware Libertarian party cross-endorsed two Republican nominees for the legislature, and the Republican Party did not object to that. Of course, in the 2008 case, the two nominees were registered Republicans.