Labor is poised to secure a remarkable victory in a by-election for the Adelaide seat of Fisher.

With the final result unlikely to be declared until pre-poll and postal votes are counted next week, Labor looks to have secured an eight per cent swing in a seat previously considered to be a Liberal one.

First preference votes from all nine booths on Saturday night showed Labor candidate Nat Cook edging ahead of the Liberals' Heidi Harris on a two-candidate preferred basis.

The results put Ms Cook ahead 51 per cent to 49, despite trailing in her primary vote.

ABC election analyst Antony Green says the result will cause "huge recriminations" for the state and federal Liberals.

"This is an eight per cent swing towards a 12-year-old state government in a seat Labor hasn't won since the 1985 state election," he said.

"If Labor has run a half-decent pre-poll and postal campaign, then they will win Fisher."

Mr Green said the Liberals would need to win 52 per cent of pre-poll and postal votes to claim victory, a result he said seemed unlikely.

The Liberals' primary vote was unchanged from the 35 per cent it received at the March state election when it lost to long-serving independent Bob Such, who died in October.

Early results had the Liberals firmly in front, with independent Daniel Woodyatt also polling strongly.

But Labor surged ahead after favourable polling at several large booths.

If Labor wins Fisher, it will have a lower house majority in its own right for the first time since Premier Jay Weatherill scraped to power at the March state election.

A Labor win would prove a major blow to the Liberals' chances of challenging legislation and raise questions about the leadership of Steven Marshall.

Labor has only held Fisher for one term - from 1985 to 1989 - since the seat was created in 1970.

The South Australian Electoral Commission will start counting postal votes on Monday and pre-poll votes on Tuesday.