Burma's Nobel laureate Aung San Suu Kyi has won a by-election for parliament, her party says, after a landmark vote which saw 45 seats contested. Ms Suu Kyi's opposition National League for Democracy (NLD) said she had easily won the vote in Kawhmu, though official counts have not yet finished. The NLD was competing in its first elections since 1990. The vote is a key test of promised political reforms, though the military-backed ruling party remains dominant. During the campaign, foreign journalists and international observers were given the widest access for years. The European Union hinted that it could ease some sanctions if the vote went smoothly. "We hope the whole day can be run in a peaceful way and we'll make an evaluation later on the basis of all the polling sessions that we will be seeing," EU observer Ivo Belet said. BBC correspondent Rachel Harvey, in Burma, says the NLD alleged some voting irregularities in the capital, Naypyidaw. A NLD spokesman told AFP news agency he had sent a letter of complaint to the election commission over allegations ballot forms had been tampered with. Nyan Win said there had been complaints that wax had been put over the check box for the party, which could later be rubbed off to cancel the vote. "This is happening around the country. The election commission is responsible for what is occurring," he said. Burma's current government is still dominated by military and ex-military figures from the old regime that ruled the country for decades and was accused of widespread rights abuses. But since 2010, when a transition to a new generation of leaders began, the government has impressed observers with the pace of change. Most political prisoners have been freed, media restrictions have been relaxed and, crucially, Ms Aung San Suu Kyi and the NLD have been persuaded to rejoin the political process. They have taken no part in Burma's political process since 1990, when the NLD won a landslide victory in a general election but the military refused to accept the result. Ms Aung San Suu Kyi spent much of the following 20 years under house arrest and refused to take part in the 2010 election, which ushered in the current reforms. The NLD is one of 17 opposition parties taking part in Sunday's election. Only a fraction of seats are up for grabs and the military-backed party will still dominate. Ms Aung San Suu Kyi, 66, was standing for a lower house seat in the Kawhmu Township constituency, outside Rangoon. On Sunday, she visited polling stations in Kawhmu before heading back to Rangoon. Earlier, Ms Aung San Suu Kyi described this year's election campaign as not ''genuinely free and fair" and warned that reforms were "not irreversible". But she said she and the NLD did not regret taking part. "Still we are determined to go forward because this is what our people want," she said. A small number of representatives from the Association of South-East Asian Nations (Asean), along with the EU and US, have been invited to observe polling. More than 100 foreign journalists are believed to have received permission to cover the vote.