document: Four constituents raised the action under the Representation of the People Act 1983.
  They argued he misled the electorate over a memo claiming SNP leader Nicola Sturgeon would rather have seen David Cameron become prime minister.
  Judges have ruled that there will now be a "By Order hearing" to discuss the next part of the case.
  Lady Paton and Lord Matthews had heard a preliminary legal debate at a special Election Court, which examined three questions.
  The first was whether section 106 of the act - which makes it illegal to make or publish false statements about any candidate during an election campaign - could apply to candidates talking about themselves, as well as attacks on their rivals.
  The judges have ruled that the language used in section 106 was "wide enough to encompass a statement made by a candidate about himself".
  However, they said they wanted to hear evidence about the two remaining issues before issuing a determination on the case.
  These are whether the words were false statements of fact which related to Mr Carmichael's personal character or conduct, and whether they were said "for the purpose of affecting the return of any candidate at the election".
  The judges said they wanted to hear evidence on these issues because each case had to be considered on its own facts.
  Lady Paton said: "Circumstances can be envisaged where a false statement of fact is of such a nature that the effect in relation to a candidate's personal character or conduct transcends the political context.
  "The question of the type of relationship between the statement and the personal character and conduct of the first respondent is one which requires evidence, including evidence as to the motive or reason for giving the false statement."
  Mr Carmichael's QC had asked the judges to dismiss the case, on the grounds it was "irrelevant" and "bound to fail".
  Legal argument was heard at a special election court in Edinburgh earlier this month, which was broadcast and streamed online live.
  The case is believed to be the first of its kind in Scotland for 50 years.
  It arose from a story in the Daily Telegraph at the start of the general election campaign in April.
  Mr Carmichael - Scottish Secretary in the Tory-Lib Dem coalition before the election - had authorised the leaking of a civil service memo suggesting First Minister Nicola Sturgeon had told the French ambassador she wanted David Cameron to remain in Downing Street.
  He claimed in a TV interview the first he had heard of it was when he received a phone call from a journalist.
  However, the MP later admitted full responsibility for sanctioning its release, and accepted the "details of the account are not correct".
  The constituents who brought the petition were aided by crowd funding.
summary: A legal challenge to Alistair Carmichael's election as MP for Orkney and Shetland is to proceed.