Toby Webster toured Edinburgh's galleries last weekend. The founder of Glasgow's Modern Institute took in Tony Swain and Nick Evans' shows at Inverleith House, two floors of art created from newspaper cuttings and sculpture, followed by Alan Michael's Pop Art paintings at the Talbot Rice gallery.

"It was nice to see some Glasgow artists on display," he said upon returning west. "Here there can be less to see."

Webster's aside is telling. For at least 10 years the contemporary visual art produced in Glasgow has been considered among the best in the world, some would say the best. The city's Simon Starling won the Turner Prize in 2005, following in the footsteps of video artist Douglas Gordon. Jim Lambie, another of Glasgow's favourite sons, is opening an exhibition in New York's Museum of Modern Art this month. At the Venice Biennale last year, the Scotland stand was dominated by Glasgow artists. Around the world at art fairs from Basle to Mexico City and beyond, Glasgow is synonymous with cutting edge, exciting work.

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But according to a growing number of buyers and curators, you wouldn't know this if you lived in the city. The disparity between Glasgow's international standing and the visible evidence in its public spaces has led one top patron from the city to say he is "ashamed".

Others have said there is a vital tier of spaces missing in Glasgow which means the public have to travel at least to Edinburgh to see the world-class work being produced in their own postcode.

The Modern Institute is the city's oldest commercial gallery for contemporary art. Founded 10 years ago, it is housed in a tenement office building just off Argyle Street. A giant, angular teacup currently sits in its exhibition area.

The space Webster can offer over to such exhibitions is bigger than most studios, which Glasgow has in abundance and is the lifeblood of the artistic community. But what is missing, he says, is the next tier up in terms of size to bring the work to a bigger audience.

"Glasgow needs somewhere bigger, that will show more and do bigger shows, like a Kunsthalle-style space," he says, referring to a building to house temporary exhibits, frequently from local artists, that are common in Germany and Switzerland. "Glasgow needs to step up. It is getting a lot of mileage internationally from what the artists are doing but it isn't always reflected here in those terms. It's simply not."

The Modern Institute is also involved with Glasgow International (Gi), the city's biennial celebration of contemporary art which runs from April 11-27. This year it has 42 shows including works by Lambie and Starling. But Webster said something more regular is needed rather than an explosion of contemporary art on Glasgow every two years.

"Gi is a step towards it but you need something more permanent and contemporary in terms of actual space. It would be nice to show the local scene, what's going on, who's doing what."

A major part of Webster's job, and of his nine staff, is to organise shows abroad for artists he works with, including Starling and Lambie. The irony of him working mainly abroad with Glasgow artists isn't lost on him.

"Since I started working in it, there's definitely a lot of artists who are exhibiting and important parts of other cities' cultural programmes," he said. "That's a big thing, when here wouldn't necessarily reflect that."

He is preparing for Lambie's New York show, which is creating a buzz in Manhattan, a Starling show in Toronto and Cathy Wilkes in the Milton Keynes Gallery in April, as well as attending the Armory art fair in New York next month.

Hugo Brown is a major patron of contemporary arts. The Partick-born engineer splits his time between Glasgow and The Hague, and keeps his 600-strong collection between the two cities. He attends art fairs such as Armory and recalled a conversation at one.

"I was at the Berlin Forum and someone said to me, Glasgow is the cutting edge of the world when it comes to contemporary art. And I thought, if only you knew'. I feel ashamed.

"People think Glasgow is the cutting edge because there are so many terrific artists who have won the Turner Prize that have come from Glasgow. They are all known outside the city. Maybe due to the Modern Institute and Sorcha Dallas, it's becoming better, but aside from those two galleries there's nowhere to show contemporary art in Glasgow."

While international demand for Glasgow's artists have meant commercial galleries have flourished over the past five years (there is one more dealing in contemporary art - Mary Mary) the main public spaces in Glasgow have "gone off the boil" according to Susanna Beaumont, an influential art curator and gallery owner. She represented four of the six artists from Scotland at the Venice Biennale last year and runs Doggerfisher gallery in Edinburgh.

"When I'm in Glasgow at least once a week to see my artists, no public spaces feature in my trip," she said. "A few years ago it would have been very different. I would have gone to Tramway and CCA. It's not as buoyant as it once was."

Tramway had well publicised financial problems and flirted with extinction while CCA, according to Beaumont, "just had a lousy director". She added: "It used to have such a big following; it was just round the corner from the art school. But it went horribly wrong, shrinking the gallery space. And then the previous director slaughtered it."

Tramway is safe, refurbished and has appointed a new director, Sarah Munro from the Collective Gallery in Edinburgh.

Francis McKee is the director of CCA and Glasgow International (Gi). He acknowledged that his institution has taken time to recover, and he hoped Gi would be a way for CCA and Tramway to be known "for all the right reasons," such as bringing contemporary art to the public.

"It's one of the country's great success stories," he said. "We keep looking at the football team in the hope they're going to do something. We follow anything in the hope Scotland's going to do something. And one of the major success stories is art, where it's well proven again and again. And it's unknown.

"Gi wants to start generating collectors in Scotland. We want people to start getting excited about art, so they want to start collecting it. It's a great shame that Modern Institute, Sorcha Dallas or Mary Mary are selling most of their artists abroad. It's crazy. People here are buying God knows what. Fancy cars? But they aren't investing in contemporary art."

Glasgow City Council defended its record on supporting contemporary art.

Mark O'Neill, head of arts and museums for the city said: "Outside London, Glasgow provides the best range of display opportunities for artists at all stages of their career.

"As well as well known names such as GoMA, Gi, Tramway and the CCA, there are numerous other artist-run spaces, such as Transmission, which receive funding from the city. The most exciting project is Trongate 103. Glasgow City Council is investing £8m on this stunning refurbishment which will house eight visual arts organisations and incorporate 10 gallery spaces."

A spokeswoman for the council highlighted a new initiative dedicated to programming contemporary art, The Common Guild.

Yet Katrina Brown, the director, said the Common Guild was formed because of the gap in the contemporary art market that Webster and Brown had highlighted.

"Glasgow is home to some world-class artists who have worked internationally for many years, but that's not necessarily reflected by the presence of contemporary visual art in the city. It's a well accepted fact that Glasgow is the most vibrant place for artists in the UK outwith London. If you looked at the scope, scale and variety of spaces in London, public and private, and compare it with Glasgow there's a massive difference."

The Common Guild is without a dedicated space, but Douglas Gordon has gifted an apartment in Park Circus for exhibitions for a year.

With the formation of the Common Guild, Gi on the horizon, new directors at the CCA and Tramway, and GoMA announcing a new fund to buy contemporary art, public spaces in Glasgow seem to be attempting to catch up with its artists. Until then even Brown admits she will have to travel elsewhere.

"People always say they have to go elsewhere to see exhibitions. People would go up to Dundee to see the DCA's latest by an artist from New York or Warsaw," she said. "And then it's only Scotrail who benefit."