The towns that dot the Danish landscape are small and quiet. They seem unlikely to generate much travel.

Yet, in January 2003, Arriva, one of the UK's largest bus and train operators, took over passenger rail services in much of central and northern Jutland from DSB, the national railway company, on a seven-year franchise.

The step, which handed Arriva operation of 15 per cent of Denmark's passenger rail network, Arriva took over operation of 35 diesel trains on the mainly single-track routes that link the region's towns to each other and to Aarhus, Denmark's second city.

It is due to receive about £150m in subsidy over the franchise's life.

The move makes Denmark the latest European country to put operation of subsidised train services out to tender. There have already been similar moves in Germany, Sweden and the Netherlands.

It is also the latest of many small steps towards the liberalisation of Europe's rail market, which is being driven by European Union legislation. The process has so far mainly affected freight, where, since March 2003, operators have had the right to operate international freight services anywhere in the EU if they have the required licences.

Liberalisation is intended to make rail transport generally more competitive, weakening the national monopolies that dominate railways everywhere in Europe except the UK.

Nevertheless, although liberalisation is slowly making Europe's railways more like the privatised British railways, Arriva is the only large UK train operator so far to show serious interest in running trains in mainland Europe.

The only other UK transport company running passenger rail services in mainland Europe is the Aim-listed GB Railways, recently bought by First Group. It manages passenger services in Estonia, which joins the European Union this year.

Eurotunnel, the Channel tunnel operator, has asked the French government for a licence to run freight trains from Lille in France through the tunnel to the UK.

Beyond these exceptions, operators are mostly sceptical about entering the continental European rail market.

Phil White, chief executive of National Express, the UK's largest passenger train operator, says shareholders would think he was "cracking up" if he suggested such a move.

The franchises being offered in continental Europe - typically short, lightly-used regional lines or networks - are too small. "We don't want to be in business in small ways," Mr White says. "Small ways lead to big problems."

Moir Lockhead, chief executive of First Group, the bus and train operator, says his company remains focused on the UK and North America.

It cannot ignore trends in Europe but would want to find a local partner for any bid. "Part of our strategy has always been to make sure that, if we go into a new market, we don't go into it blind."

Unfortunately for Arriva, the early stages of its Danish operations illustrate some of the market's potential pitfalls.

In Silkeborg, in Jutland's lake district, Arriva managers explain how an unexpected surge in absenteeism wrecked their calculations about how many drivers they needed.

DSB - which was facing driver shortages of its own - declined to help out with spare drivers, even though it had undertaken to help with any shortages after the handover in January 2003.

"There was an underestimation of the difficulties that were going to be created by the handover," says Piers Marlow, Arriva's passenger services director for Northern Europe. And Arriva faced vilification in the Danish press as it was forced to cancel many trains or replace them with buses.

The problems were solved only in April, when DSB took back operation of one of Arriva's six routes for eight months to allow Arriva time for further driver training.

Yet Arriva insists it was still right to start its Danish rail operations.

In recent months, it says, Arriva's punctuality has been better than DSB's. In 2004, it expects to receive 29 new trains to replace those it now rents from DSB.

Bob Davies, Arriva's chief executive, argues that the company carries only limited risk if patronage fails to rise and that the £150m subsidy substantially offsets that risk.

The company - which made pre-tax profit of £80.6m on £1.39bn sales in 2002 - will not discuss precise profit figures for its Danish operations. And other UK train operators fear the risks in mainland Europe would outweigh the rewards. Their rivals would typically be dominant, well-connected, state-owned and have a better understanding of market conditions.

Only the UK's train leasing companies seem immune to such pessimism.

Angel Trains, the leasing subsidiary of Royal Bank of Scotland, believes it now leads mainland Europe's market in train leasing.

Angel now has trains worth €440m (£307m) operating or on order throughout Europe.

Haydn Abbott, Angel Trains chief executive, says that, where operators risk losing services through franchising rounds, they want the flexibility of leasing.