Mr Kennedy must show that Lib Dems can appeal to the centre as well as the margins

The Liberal Democrat leader, Charles Kennedy, has cut a thoroughly positive figure in the run-up to his party conference this week in Bournemouth. He has capitalised impressively on his party's opposition to the war in Iraq, helped - admittedly - by the embarrassing efforts of Tory leaders to wriggle out of their ill-conceived stance on the war. He has also benefited from an unusually strong front-bench team, with special mention due to the Foreign Affairs spokesman, Sir Menzies Campbell. The result is a cogent and considered manifesto.

The Liberal Democrat leader, Charles Kennedy, has cut a thoroughly positive figure in the run-up to his party conference this week in Bournemouth. He has capitalised impressively on his party's opposition to the war in Iraq, helped - admittedly - by the embarrassing efforts of Tory leaders to wriggle out of their ill-conceived stance on the war. He has also benefited from an unusually strong front-bench team, with special mention due to the Foreign Affairs spokesman, Sir Menzies Campbell. The result is a cogent and considered manifesto.

So when Mr Kennedy says, as he has done in pre-conference interviews, that the party is poised for an electoral breakthrough, this is no idle day-dream. It is a reasonable expectation, which is also confirmed by recent opinion polls. As Mr Kennedy has also said, however, and repeated yesterday, this depends on the party presenting a credible alternative to what is already on offer. And that requires the Lib Dems not only to have policies that set them apart from the other two main parties, but to have a policies and leadership package that makes them a plausible party of government. This is where Mr Kennedy still has work to do.

For all the gains made by the party in recent elections, it has failed to move convincingly or consistently into the second slot behind Labour. In the European elections, it had to settle for fourth place behind the UK Independence Party. This was not the result for which it had hoped.

Support for the European Union, its principled opposition to the Iraq war and its courageous stance on immigration are all policies that set the Lib Dems apart. On these issues, unlike Labour or the Tory party, the Lib Dems are united. They have no need of the parsing and qualifying that the other two parties have to apply. On foreign policy, the Lib Dems already present a credible alternative.

They are advancing in that direction on the economy as well. Their pre-election manifesto presents a carefully calculated set of policies, many of which make a great deal of sense. These include the proposal that many government departments, including the Treasury, should be moved out of London. And this is not cutting for cuts' sake, it is part of a wider policy to devolve much more control to the regions. This is responsible and bold; it is also something many people would probably support.

It is with the party's tax and spending proposals that the first misgivings arise. The notion of abolishing council tax, introducing a local income tax and raising the upper rate of income tax has more than superficial appeal - especially to the lower paid and pensioners. Several of the party's spending proposals are also eye-catching, including the abolition of charges for long-term care for the elderly.

The question here, however, is whether the sums add up quite as the Lib Dems say they do. Just as the lower paid and pensioners would, by and large, benefit, so middle-income earners could find themselves doubly penalised. Yet it is, by and large, middle-income professionals who are starting to lose out under the current system, too, because of the proliferation of means-tested benefits.

Nor, as the British and US experience has so graphically shown over the years, do higher taxes necessarily lead to a higher "take" for the Exchequer. The reverse can be true. The better off can afford better advice and more effective shelters for their income. It is not apparent that the Lib Dems, who tend to think the best of humanity, have necessarily thought this fully through.

Mr Kennedy goes into his party conference stronger, personally and politically, than for many a year. To achieve the "breakthrough" he has so striven for, though, he needs to show not only that the Lib Dems' arithmetic is correct, but that he and his party can appeal to the mainstream - to all those voters whom New Labour and the Tories have managed to alienate between them. Mr Kennedy's task for the week is to show that he can broaden his party's appeal and make the Lib Dems the credible alternative they deserve to be.