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ABC Incoming Tasmanian Premier Will Hodgman addresses supporters as his wife, Nicola, shares a laugh.

Labor has been swept from power in Tasmania but is clinging to life in South Australia after both states went to the polls on Saturday.

Voters called time on 16 years of Labor rule in Tasmania, flocking to the Liberals, whose leader, Will Hodgman, had positioned his party as the only option for a stable majority government.

The Liberals will get that, with at least 14 seats in the 25-seat legislature, which is decided using the complex Hare-Clark proportional representation system.

Premier-elect Mr Hodgman said Tasmanians had voted for change "and that's what they will get".

In South Australia, what had been expected to be a comfortable Liberal victory failed to materialise, with Jay Weatherill's Labor putting up a fight in the Adelaide marginals which have delivered it power for the past three terms.

The South Australian Electoral Commissioner says with the high volume of early and postal votes, up to a quarter of the overall vote is yet to be counted.

The ABC's election computer is predicting 23 seats for Labor, 21 for the Liberals and two for independents.

Both major parties say the seat of Mitchell is too close to call.

Mr Weatherill said he was "hopeful of retaining government".

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Liberals swept to power in Tasmania, Labor hopeful of clinging to power in South Australia