"The Persistence of Vision", by John Varley won both the Hugo and Nebula for Best Novella, awarded in 1979 for work of 1978. (The 1979 Worldcon was the first one in Brighton.) The second paragraph of the third section is:

It was substantial enough that I felt it would be unwise to crawl over it. I had crossed many wire fences in my travels and not got in trouble for it yet, though I had some talks with some ranchers. Mostly they told me to keep moving but didn’t seem upset about it. This was different. I set out to walk around it. From the lay of the land, I couldn’t tell how far it might reach, but I had time.

It's a story set in the near future (the 1990s) in a disintegrating United States; our narrator, trekking across the country, encounters a community in New Mexico where all the adults are blind and deaf, and therefore have access to spiritual enlightenment and ultimately (it appears) physical ascension to another plane of existence. The depiction of a human society made up of people very nearly like most of humanity, but establishing a sort of utopia, is beautifully done, and obviously wowed the voters for both awards. It's an appeal for a better kind of society, and for not looking down on disability.

I have to say that while I agree about not looking down on disability, to portray it as a supernaturally liberating experience may not be terribly close to the lived experience of people with disabilities. I can see where Varley is coming from as a literary device, but it doesn't really speak to me.

His narrator is also rather frankly relaxed about sex with underaged teenagers.

A story that has shown its age.

The original F&SF issue with "The Persistence of Vision" is available here.

Dreamsnake, by Vonda N. Mcintyre, won both the Hugo and Nebula for Best Novel, awarded in 1979 for work of 1978. When I first wrote it up in 2001, I said (dead links removed, some commentary added):

The first chapter, originally published as "Of Mist, and Grass, and Sand" won a 1973 Nebula in its own right for Best Novelette. That must make it the only text to have won either Hugo or Nebula twice, once on first publication and again on inclusion in the longer work.

Dreamsnake is the story of a healer called Snake, who heals people with the serum of genetically modified snakes. In the first chapter she loses her dreamsnake, a rare and almost irreplaceable creature. The rest of the book has her wandering through desert settings and towns to try and find a replacement, adopting Melissa, a girl who has suffered mutilation and sexual abuse, being ejected by the hi-tech city called Centre, and finally discovering the secret of the dreamsnakes while evading enslavement by a bad guy. She is rescued at the end by a bloke called Arevin who she met in the first chapter.

The setting of Dreamsnake is quite remarkable. Most readers pick up on the fact that it is a depopulated Earth many years after an almost forgotten nuclear holocaust. However, much more important is that the big issues of human sexuality have been almost completely sorted out. Both men and women can control their own fertility by "biocontrol"; polyamorous relationships are accepted as everyday; women are leaders of desert tribes (though men seem to be in control in the few towns). The gender of one character is left completely unspecified, leading some readers to conclude that he/she must be a hermaphrodite. I don't think this is the case, since such individuals are not mentioned elsewhere in the  novel (compare the direct way in which Ursula Le Guin and Lois McMaster Bujold present this issue); instead I agree with Ursula Le Guin that the author is challenging the reader to ask why we need to know Merideth's gender in the first place. [On reflection, these options are not mutually exclusive. ]

This could have been a utopian setting, in which the author preached the superiority of a world where women are not oppressed. However it is not. Snake has to deal with superstition, radiation poisoning, crime, child abuse, drug abuse, abuse of power and above all disease as she travels across the blasted heaths of her world. The bad guys do tend to be men but so are some of the good guys. The most utopian aspect is the low-tech environment, compensated for by the advanced biological techniques of the healers who are in harmony with nature.

This novel has one great character and many great ideas. My biggest disappointment is that the plot is rather disjointed; you can see the seams. The expedition of Snake and Melissa to the walled city of Centre which appears to be the main thrust of the middle of the book turns out to be a fools' errand. The actual venue for the book's climax has not been signalled at all in advance, so it feels rather as if the author was making it up as she went along. The only bit of the end that has been prefigured is the reappearance of Arevin, who literally rides in to  save the day in the last few pages, fatally undermining the feminist themes of the book as he does so. Compare Guy Gavriel Kay's The Lions of Al-Rassan, also about a female healer in a less primitive, more violent environment, which is a much more tightly plotted novel. (Actually I think the two make a good paired reading.)

Susan Stepney sent me an email chiding me for my interpretation of Arevin's role at the end of the book. Her own reading is more generous: "Arevin doesn't save the day. He rides in after Snake has defeated North, and after she has rescued herself and Melissa. All he does are "nurturing" things. He prepares some "medicine" for Melissa —
but under Snake's instruction. He cleans Snake's wound — but not well enough, and she knows she'll have to do it again herself. He's merely there to show Snake's reconnection with the world, her gradual allowing of others to do things for her. Well, that was my reading, anyway :-)"

The world has moved on since the 1970s. It's difficult to conceive of any serious sf book now set on a devastated post-nuclear holocaust Earth; the end of the Cold War sank that particular nightmare, though 11 September 2001 gave us new ones. [Not to mention climate change, and 2020's own particular circumstances.] Of course, this is a utopia (if a cautious one) so we should not make too many demands in terms of realism.

Not a lot to add to the above, except to say that it was an interesting paired reading with "The Persistence of Vision" – both somewhat post-apocalyptic novels, with new visions for human society, which are presented as egalitarian but nonetheless have their limitations. You can get Dreamsnake here (it’s back in print again).

The Best Novel final ballot for both Hugo and Nebula also included Blind Voices, by Tom Reamy and The Faded Sun: Kesrith, by C. J. Cherryh. Hugo voters also went for The White Dragon, by Anne McCaffrey and Up the Walls of the World, by James Tiptree, Jr., but the latter was withdrawn. I’ve read all of them and would probably have voted for Dreamsnake. I have read neither of the other two Nebula finalists, Kalki, by Gore Vidal and Strangers, by Gardner Dozois.

The only other Nebula finalist for Best Novella was “Seven American Nights”, by Gene Wolfe. It was on the Hugo ballot too, as were “Enemies of the System”, by Brian W. Aldiss, “Fireship”, by Joan D. Vinge and “The Watched”, by Christopher Priest. I have an affection for the Aldiss story.

The Hugo for Best Novelette went to “Hunter’s Moon”, by Poul Anderson, and the Nebula to “A Glow of Candles, a Unicorn’s Eye”, by Charle L. Grant. “Devil You Don’t Know”, by Dean Ing and “Mikal’s Songbird”, by Orson Scott Card were on both lists (neither winner was on the other ballot).

The Hugo for Best Short Story went to “Cassandra”, by C. J. Cherryh, and the Nebula to “Stone”, by Edward Bryant. Both winners were on both shortlists, but there were no other crossovers. The Nebula ballots were very short that year, only two for Best Novella, and three for Best Novelette and Best Short Story.

The Hugo for Best Dramatic Presentation went to Superman.

Next up in this sequence are the following year’s three joint winners: “Sandkings” by George R. R. Martin, “Enemy Mine” by Barry B. Longyear and The Fountains of Paradise by Arthur C. Clarke.