One of the strangest contests in Minnesota political history got even stranger Thursday with reports that Republican gubernatorial candidate Jon Grunseth was stepping down.

Grunseth`s campaign to unseat the two-term incumbent governor, Democrat Rudy Perpich, was mortally wounded last week by allegations of sexual misconduct nine years ago at a party in his suburban St. Paul home.

Grunseth, 44, had been under increasing pressure from his party to quit the race after two women charged in sworn statements that a nude and intoxicated Grunseth encouraged them to join him in a nude swim in 1981, when they were 13 and 14.

On Monday, another odd twist added more pressure:

Arne Carlson, a maverick Republican moderate whom the conservative Grunseth soundly defeated in the primary, re-entered the race as a write-in candidate.

''When there are three people in the race, and two of them are Republicans, the voter base is not big enough to accommodate that. So we`re heading down the wrong road,'' Sen. Rudy Boschwitz (R-Minn.) told reporters Wednesday upon arriving from Washington.

While support for Grunseth among leaders of the party`s central committee has remained strong, Republican candidates and the party`s few elected officials expressed concern that Grunseth`s problems would affect their campaigns.

Boschwitz`s re-election bid, for example, is facing a surprisingly strong challenge from Democrat Paul Wellstone. So Thursday afternoon, Boschwitz went into a long huddle with state party chairman Robert Weinholzer.

Then, shortly before 5 p.m., it was announced that Grunseth would hold a news conference at 7 p.m. Rumors were rampant among political consultants that Grunseth would step down if the party would name a candidate of his choice to the ballot in his place.

Grunseth was said to have ruled out Carlson, whose chances of beating Perpich as a write-in candidate are considered to be worse than slim. Instead, it was widely rumored that Grunseth wanted Cal Ludeman, a kindred conservative who ran against Perpich in 1986.

But as the evening wore on, scores of reporters and news crews were waiting, while Grunseth was said to be in heated debate with his campaign staff and fundraisers.

By late Thursday night, no official announcement on Grunseth`s status had been made.