Stephen Watkins gained custody of his sons, aged 8 and 10, after he split with his wife Edyta. She and the boys vanished in March 2009 only to emerge two years later in Poland, her native country.
Watkins was in court today appealing a Polish ruling made last year which decided against sending the boys back to Canada.
The 40-year-old Newmarket, Ont., man says the court will make an announcement on his case on May 29.
Prime Minister Stephen Harper discussed the case with his Polish counterpart earlier this week when Donald Tusk was on Parliament Hill.
Harper has said the government has been providing consular assistance to enforce Canadian court orders in the case, and Tusk has hinted the Polish government won't stand between Watkins and his sons if the Canadian man wins his day in court.
A Canada-wide arrest warrant for abduction was issued for Watkins' ex wife in 2009, and her name appeared on the RCMP's most wanted list. York Regional Police allege the mother and children drove into the U.S. and then flew to Germany.
In the summer of 2011, she and the boys were tracked down in Poland, but last December, a Polish court ruled against sending the boys back to Canada.
The ruling was based on a conclusion that it would be detrimental for the children to return to Canada as they had integrated fully into Polish society.
Watkins has maintained his sons still speak more English than Polish and that he has secured the support of Canadian agencies that would help his sons re-settle into their home in Newmarket.
He argues that Poland has recognized Canadian court orders that show he has sole custody of the children and has acknowledged that international law had been broken.
Poland doesn't have an extradition treaty with Canada, but is party to the Hague Convention, which is meant to expedite the process of returning abducted children.