The Swedes are hoping for more than a greater awareness of their programs treating drug and alcohol abuse to come out of Nancy Reagan's two-day trip to Stockholm next week. They also hope Mrs. Reagan's visit, the first ever by an American first lady, will lead to an invitation from President Reagan to King Carl XVI Gustaf to make a state visit to Washington next April.

The State Department, which advises the White House on these things, is between a rock and a hard place on this one. Complicating matters is the official visit to Washington in September by Sweden's Prime Minister Ingvar Carlsson, the first by a Swedish PM in 25 years. Even though Reagan has proclaimed 1988 the Year of New Sweden, to invite the king and queen to make a state visit so soon after Carlsson would almost certainly infuriate the Finns, who are also lobbying for a state visit.

Carl Gustaf and Queen Silvia are already planning to be in the United States to open the yearlong celebration marking the 350th anniversary of the first Swedish colony in North America. Much as Britain's Prince Charles and Princess Diana did in 1985 with the "Treasure Houses of Britain" show at the National Gallery of Art, Sweden's royals will unveil spectacular exhibitions at three major museums here, including "Sweden: Arts for the Crown" at NGA. (They will also visit 16 other American cities.)

The Reagans gave a glittering dinner at the White House for Charles and Diana. It wasn't a state occasion since Charles isn't yet king, but an invitation proved to be even more sought after than one to a state dinner.

By extending similar hospitality to Carl Gustaf and Silvia, thereby placing them in an exclusive White House category reserved for visiting royalty, the Reagans probably would get the State Department off the hook.

And who knows, the Swedes might even have more fun.

While Mrs. Reagan is in Stockholm, she will lunch with Queen Silvia and meet Ingrid Carlsson. But she'll also visit with expectant mothers who have drug problems and attend a musical by a group of artists against drugs. It will be the eighth time she has taken her anti-drug abuse campaign abroad.

Leader Dole, which is to say the top dog in Sen. Bob and Transportation Secretary Elizabeth Dole's household, had a press conference the other day. Not to announce his candidacy for president but to proclaim his support for another dog-eat-dog contest, the third annual Kal Kan Capital Canine Follies benefiting the Capitol Children's Museum.

Among the fascinating revelations by Leader, a self-made mutt resembling a miniature schnauzer, who was given a new leash on life by the Washington Humane Society: The show not only helps raise money for a worthy cause, "but it is also one of the few times I get to see my masters together.

"Let me tell you," Leader continued in remarks read for him by Elizabeth Dole at the session in her husband's Senate office, "the Doles have been very good to me. Sure, they argue once in a while over which one is going to take me for a walk when I need a breath of fresh air in the middle of the night, but believe me, their bark is much worse than their bite."

Leader is chairmutt of Saturday's fund-raiser (the museum has time and ticket details) at the Embassy of New Zealand. Other big name "dogmacrat" and "repuplican" power pups scheduled to be shown include Boxcar Willie Reagan-Revell; McTavish, Cinder and Bonnie Lott; Bentley-Steele Pressler and Woodrow Wilson and Daniel Webster Solarz. At 27, he's Washington's youngest expert on American first ladies. Now, after 10 years of research and six years at the typewriter, Carl Sferrazza's determination to publish a book about his findings is about to pay off.

"Ladies First: The Power of the Presidents' Wives," the book he's been working on since he was a senior in high school, has been bought by William Morrow and Co. for a reportedly substantial though undisclosed sum. Amid expectations that the book will become the definitive work on the subject, Morrow editors have set publication for January 1989, to coincide with the next presidential inauguration. Working with Sferrazza as his editor is Lisa Drew, vice president and senior editor of Morrow, who also edited Alex Haley's bestselling book "Roots."

A graduate of George Washington University, Sferrazza says "Ladies First" covers 200 years of "first ladyship" history, with the focus on 15 presidents' wives. Sferrazza, whose nom de plume will become Carl Sferrazza Anthony by switching his middle and last names when "Ladies First" is published, is also winding up research on a book about Florence Harding and her friendship with Evalyn McLean, owner of the Hope diamond, one-time co-owner of The Washington Post and self-acknowledged morphine addict. His play, "Diamonds and Pearls," about Mae West and Alice Longworth, will have a fully staged reading this fall by Georgetown Workshop Theater. In Leningrad and Moscow, he was almost a cult figure, stopped on the street by admiring Soviet citizens wanting to talk about his art.

This month Jamie Wyeth comes to Washington for the opening at the Corcoran of "An American Vision -- Three Generations of Wyeth Art," the collection of 103 works painted by Jamie, his grandfather N.C. and his father Andrew that brought out Soviet art lovers in record-breaking numbers for three months.

Jamie and his wife Phyllis made two trips to the Soviet Union, where not all their time was devoted to being interviewed on television. They also met with young Soviet dissidents on several occasions.

AT&T will underwrite a gala dinner on June 30; the next night Nancy Reagan will open the show to the public.