The case was sparked after Labour's National Executive Committee decided that full members could not vote in the leadership election between Jeremy Corbyn and Smith if they had not had at least six months' continuous membership up to July 12 - the "freeze date".
In order to vote members had to make a payment of £25 between 18 and 20 July.
When the decision was made anti-Corbyn groups welcomed the decision, while those aligned with Corbyn, including Momentum, have said the changes were made to rig the election in favour of the challenger candidate.
After near 130,000 members were excluded, five new members brought the case forward, arguing that they would play an important role in the contest.
It is thought that many members who joined the party since the general election last May did so to support Corbyn.
The claimants dispute that the Labour Party rulebook allows such a restriction, and the outcome of the case should determine the rights of tens of thousands of new members to take part in the election and the nomination process to be held shortly by constituency parties.
Corbyn is still the strong favourite in the election, with pollsters and bookmakers backing the incumbent to retain his job.
The fallout stems from Labour MPs' lack of confidence in their leader following what was widely considered a lacklustre EU referendum campaign. Others are scared that he'd stand no chance in a general election and is not providing effective opposition to the government.