Young Marble Giants never meant to reform.

In truth, the Cardiff trio, who play their first ever Glasgow show on Monday night, had been barely there in the first place. The band's sole long-playing release, Colossal Youth, whose title was also designed to suggest images of ancient Greek statues, seemed to have come fully formed from nowhere when it was released by Rough Trade records in 1980.

The record's collection of 15 austere vignettes sounded like nothing else around. Brothers Stuart and Philip Moxham weaved clipped, scratchy guitar and bass patterns around singer Alison Statton's fragile, untutored voice, as she sang Stuart Moxham's lyrical fragments with a distance that made them sound like the darkest of nursery rhymes. A drum machine and occasional organ added to the eeriness, as did the shadowy image of the trio on the album's suitably stark cover. The term "lo-fi" doesn't come close to describing their style.

"We didn't think it was going to get anywhere," says Stuart Moxham today. "We were on the dole and living in what was practically a squat, and were desperate to get out of Cardiff. It seemed everyone else was making this loud thrashy noise, so we decided to turn things around and go the other way."

"Let's Hear It For Quiet Music" ran the headline on one rapturous review of Colossal Youth as Young Marble Giants became critical darlings of the underground musical landscape. A follow-up EP was led by the song Final Day, later covered by Belle and Sebastian, and the band toured Europe and America.

By the time they released Testcard, a second EP featuring six brief instrumental sketches, Young Marble Giants had vanished into the ether from which they'd seemingly sprung. In truth, the band's implosion was much more mundane.

"We'd planned for the future," says Moxham, "but there was no plan for success. Nobody tells you that being in a band is like being in a marriage, but with more people. We were very young, and we were people who couldn't really talk about things that mattered. Phil and Alison were splitting up as a couple, there was our sibling rivalry, and then Alison got really ill."

The three went their separate ways, with Statton fronting the equally short-lived nouveau pastoral jazz trio Weekend and Moxham releasing material under the name The Gist. His brother Phil played with Everything But The Girl and Pere Ubu's David Thomas. Only when Moxham was approached with a view to YMG reforming to record new material was any kind of reunion mooted. By that time, Kurt Cobain had declared them one of his two favourite bands (The Vaselines from Glasgow were the other), Courtney Love had covered their song Credit In The Straight World and Colossal Youth was about to be re-released on CD.

At that point, Statton and the Moxhams hadn't been in the same room together for 27 years. Despite Moxham having long given up on any chance of a reunion, the meeting in a Welsh pub went surprisingly well.

"Phil is the big decider in this band." says his big brother. "He's the draconian filter, and he and Alison both said yes really easily, which was a surprise. We decided to get our other brother, Andrew, who's a brilliant musician, to join as well."

The success of what was initially a one-off appearance at the Powys-based Hay Festival of Literature and Arts led to more shows - at least those which grown-up commitments would allow for. YMG's most recent appearance was at a festival in Laugharne, the Carmarthenshire town where poet Dylan Thomas lived and was inspired to write Under Milk Wood.

While in Moxham's mind, at least, the show wasn't a musical success - "those songs have to be played not just note perfect, but with feeling, and if there's a mistake, it screams out because there's so little there," - he nevertheless had a minor epiphany.

"So now we've got three brothers and an ex-girlfriend who's really an honorary member of the family in the band," he says, "and I only realised when we were in Laugharne that this really is a family affair.

"We've been going to Laugharne since we were toddlers, and I realised that being in a band, you have to give it as much love and care as you would with any family. That was a great revelation to me. I've always had frustrations with this band, but now that I've realised that, I think it might be easier."

Seven years on from the reunion, there is still no sign of that difficult second album.

"That's another frustration," Moxham reflects. "We reformed to do this particular thing, and said we weren't going to be an eighties comeback band, but here we are. I would love to make a new record, but making music with people is like having sex.

"You have to make yourself vulnerable. We're all desperate to do it, and there's so much going on under the surface. We're all artistically and spiritually richer people since we last wrote together 34 years ago, so I hope it will happen."

Young Marble Giants play Stereo, Glasgow, on Monday.