16 December 2015 Last updated at 00:22 GMT
One bans women from marrying for six months after divorce, the other forces married couples to have the same surname.
The laws are also linked to a rule that children born within that six months are considered to be the former husband's.
The case was brought by three individual women and one couple in a civil partnership, who argue that the law is unconstitutional and discriminatory.
Two lower courts have already ruled against them and public opinion on the questions is split.

Keith Barrow quit as leader of the Conservative-run Shropshire Council and as a councillor when an allegation was made in November.
He later admitted to failing to comply with the council's code of conduct by not declaring a conflict of interest.
However, West Mercia Police said a "thorough and detailed investigation" found no case to answer.
Updates on this story and more from Shropshire
Det Insp Mark Glazzard said: "Following receipt of a complaint in November 2015, a thorough and detailed investigation was conducted...into an alleged offence under the Localism Act 2011.
"This investigation has concluded, and no further action will be taken into this matter."
Previously, West Mercia Police said it had received a complaint regarding "misconduct in public office involving a man from Shropshire". The BBC understands the complaint relates to Mr Barrow.
The former council leader stood down after failing to declare a relationship with the director of an accountancy firm appointed to work with the authority's private company, IP&E.
He apologised and also resigned as director of IP&E, following the findings of an internal investigation.
Shropshire Council did not wish to comment.

Strauss, the England and Wales Cricket Board's director of cricket, told Pietersen in May that he would not be considered for an international recall.
"I think that clarity has helped," Strauss said.
England won the Ashes 3-2 but trail 2-0 in the one-day series before Tuesday's third ODI at Old Trafford (14:00 BST).
Pietersen, 35, who was initially sacked after the 5-0 whitewash in the 2013-14 Ashes series, remains England's record run-scorer in all formats.
But Strauss believes the team has "moved on".
He added: "The danger at that time was that particular issue would overshadow everything that happened on the pitch over the course of the summer.
"What I was trying to do was provide clarity going forward so everyone knew where they stood.
"I think the team has moved on and the team is in a pretty good place. Some of those young guys have established themselves and that's what we will be focusing on taking England forward."
England have called up wicketkeeper Jonny Bairstow after deciding to rest Jos Buttler for the remaining three games of the ODI series.
Meanwhile, Australia could be forced into three changes after all-rounder Shane Watson, batsman David Warner and bowler Nathan Coulter-Nile were all ruled out of the rest of the series through injury.
County cricket trio John Hastings of Durham, Yorkshire's Aaron Finch and Gloucestershire's Peter Handscomb have replaced them.
Japan's Supreme Court is due to rule on two 19th century family laws which critics say are sexist and out-of-date.
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A complaint against a former council leader has been disregarded by police.
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England are benefiting from the decision to exclude former batsman Kevin Pietersen from selection, says English cricket chief Andrew Strauss.