Hundreds of Conservative members have been reportedly been sent more than one ballot paper to vote for the next party leader and prime minister.
One party insider said more than 1,000 people could have received multiple forms to cast their vote in the leadership contest.
Ballot papers have been dispatched to around 160,000 Conservative Party members around the country to choose between Boris Johnson and Jeremy Hunt.
But some have received two ballot papers, in some cases because members live and work in different constituencies and may have joined local Conservative Associations in both areas.
People who have changed their name, after marriage for example, may also have been affected, BBC Radio 4's Today Programme found.
Iain Duncan Smith, chairman of Mr Johnson's campaign, said the Tory Party needed to address the problem to prevent duplicate votes.
"Obviously there is an issue here, I accept that," he BBC Radio 4's Today programme, adding that he was sure party chairman Brandon Lewis was looking into it.
The former Tory leader added : "In all elections there are issues about this, where people are registered separately, and in the ballot papers it's quite clear ... that you are not to vote more than once.
"But it's clear that the Conservative Party needs to continue to do some work and look into how they can actually sift this properly so that they recognise who is who."
The party has insisted anyone voting twice would be expelled.
In most elections, voting more than once would be illegal, but the leadership contest is only governed by the Conservative Party's internal rules.
The Electoral Commission, the independent body which oversees UK elections to ensure their integrity, has no role in the leadership contest.
The vote closes on July 22 and the result will be revealed the following day.
Theresa May will take her final session of Prime Minister's Questions on July 24 and make way for the contest winner that afternoon.
