Galleries in Scotland fear new tariffs will be imposed on showcasing some of the world's finest artworks due to Brexit may lead to fewer blockbuster exhibitions.

Galleries and museums are currently exempt from tariffs on the loaning of art to and from Scotland and other EU countries.

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However, post-Brexit, gallery directors and gallery registrars - who manage the flow of art to and from galleries - fear being outside the EU will lead to extra charges and bureaucracy which could stifle the staging of top-class exhibitions.

The extra costs and drain on resources will hinder collaborations with other major galleries, it is feared, and damage the free flow of art between Scotland's galleries and abroad which is key to major international-quality shows.

The self portrait show which opened this weekend at the Scottish National Portrait Gallery, Facing The World, which features art from Rembrandt to Ai Weiwei, is an example of such collaboration: it is being staged in concert with art from the Musee de Beaux Art in Lyon, France and the Staatliche Kunsthalle in Karlsruhe, Germany.

Arthur Watson, president of the Royal Scottish Academy (RSA), whose annual show opens this weekend, said: "It is very pertinent right now.

"None of these collections could have afforded to do these exhibitions without the participation of the other two.

"It is not just the extra [tariffs], other costs were often met by European funding, so it's a double hit, and I think the effects are going to be very serious."

Kathy Richmond, the chair of the UK Registars Group, said she was "very concerned" about both a possibility levying of charges on loaned art as well as the extra resources required to organise exhibitions, with costly and time consuming bureaucracy, after Brexit.

"It would really have an impact on our work," she said. "We really hope it does not lead [to fewer shows] because a lot of people are working really hard to allow art to flow between museums and galleries."

Sarah McCrory, the director of the Glasgow International visual arts festival said: "I would say that Brexit will affect the funding arts organisations are able to apply for, will impact on partnerships we might otherwise develop, and our ability to get money from the central European funds. I imagine the cost of putting on exhibitions will increase for people needing to move art around the world."

Hundreds of major art works are loaned, and are received as loans, every year at Scotland's major galleries.

The National Galleries of Scotland (NGS), for example, loaned 800 works of art to other galleries in the last year, and received 1200 in return.

Loaning and borrowing works of art is the the bedrock of 'blockbuster' summer shows such as the Surrealist and Impressionist shows being staged this summer in Edinburgh.

Inspiring Impressionism, the major show at the Scottish National Gallery, is a collaboration with the Van Gogh Museum in Amsterdam, while Surreal Encounters at the Scottish National Gallery of Modern Art has been jointly organised with galleries in Hamburg and Rotterdam.

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A spokeswoman for the NGS said: "The National Galleries of Scotland’s current process for the import/export of cultural goods is linked to both EU and UK legislation and a change to our EU status would be reflected in this process.

"It is possible that tariffs and/or duty that we are currently exempt from paying might be applied.

"The NGS will continue to monitor the situation and seek information and advocate where necessary."

A galleries source added: "There are circumstances in which NGS is exempt from certain tariffs involved in transporting artworks because the UK is currently a member of the EU.

"If UK leaves the EU these exemptions may no longer apply."

A spokesman for Glasgow Life, which runs the city's art galleries and museums, said: “We are aware of potential issues which may result from the UK leaving the European Union and we are looking at any potential implications for our future programmes."

Ms Richmond added in a statement to colleagues: "What the reality of changes to our legal framework will be as a result, and the impact on the movement of art and the movement of people in relation to our work are issues that we will need to explore.

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"It is safe to say that we have no concrete answers at this stage."Meanwhile Joanne Orr, the chief executive of Museums Galleries Scotland, said: "It is going to take time to scope the legal and policy impacts of an exit.

"We will be working with stakeholders across the UK to better understand the implications for museums and galleries and their collections and to respond effectively to potential changes."