Last year's spectacular national success by the SNP gave these local elections a significance that few could have imagined when the decision was taken back in 2007 to "de-couple" them from Holyrood elections and hold them separately some 12 months later.

Because of what happened last year the elections had become a litmus test. Could the SNP continue to sweep all before it or would they suggest that last year's achievement was but a nine-day wonder, never to be repeated? If the SNP did manage to do well, its hand in the debate about the independence referendum would be significantly strengthened. If, however, it were seen to falter, Unionists might hope to seize the initiative for the first time in months.

Yet it was a litmus test that was never going to be easy to decipher. The seats up for grabs on Thursday were previously contested as long ago as 2007, when Mr Salmond only narrowly edged ahead of Labour in that year's simultaneous Holyrood election. As a result, Nationalists could make substantial gains without performing as well as they did a year ago.

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Such a scenario was potentially ideal for Nationalist spin doctors – a golden opportunity for success to be claimed regardless of whether much progress had been made at all. Yet during the campaign the SNP invited us to judge their performance by a very simple test indeed: whether or not they could succeed in taking power in Glasgow.

This was not only a simple test, but a tough one. To become the biggest party in Scotland's biggest city the Nationalists would probably have to repeat the 8 per cent swing from Labour they secured 12 months ago – and do even better than that if they were to gain an overall majority of the city's 79 seats.

Their decision, the product perhaps of over-confidence, backfired. Not only did the SNP fail to win control of Glasgow, but they also failed to prevent Labour from reasserting its grip on the city. In the event, the swing from Labour to SNP across the city proved to be no more than four points. Glasgow's SNP leader, Alison Hunter, proved to be no Alex Salmond when it came to persuading voters it was time to give Glasgow a political makeover.

Indeed, it was not only in Glasgow that the SNP struggled to reproduce its success of last year. Across the country's largest cities, the SNP's share of first-preference votes was well down on what the party achieved in the constituency vote in last year's Holyrood elections.

Although the SNP won rather more seats than Labour, the two parties were more or less neck-and-neck in the size of their net gains. Last year's victory may not have been a nine-day wonder, but the outcome on Thursday does suggest it was an exceptional result that will never be easy for the SNP to repeat. Nevertheless, there were some significant successes for the SNP. Following the switch to proportional representation in 2007, the SNP had found itself without overall control of a single council. This time, however, the party gained control of Dundee and Angus.

Meanwhile, although Labour avoided another hammering on the scale of last May, the party still has a long way to go before it can be regarded as back in rude health. Before its first defeat in 2007, winning fewer councillors than the SNP would have been regarded as unthinkable, especially at a time when the party is in opposition at both Westminster and Holyrood and therefore not likely to be on the wrong end of an anti-government protest vote. However, the party's performance was still weaker than it had been as recently as 2003.

Equally, results brought little cheer for either of the two UK coalition partners – the Conservatives and the Liberal Democrats. Once again the Scots Tories took a step backwards, apparently suffering a drop in their share of first-preference votes and a net loss of 16 seats.

Meanwhile, the LibDems suffered a reverse similar in scale to that inflicted on them last year. Unfortunately for them this was one result that was no surprise.

John Curtice is Professor of Politics, Strathclyde University.