Accountant Murray Pringle, 74, of High Wycombe, Buckinghamshire, and Simon Pringle, 56, a businessman, of Hastings, East Sussex, both lay claim to the baronetcy of Pringle of Stichill in Roxburghshire.
The Queen has asked senior judges to make decisions on the dispute. Seven judges are analysing evidence at a hearing of the Judicial Committee of the Privy Council in London.
The hearing began yesterday and is expected to end today.
The judges, who are all Supreme Court justices, are not expected to publish a ruling until next year. Judges have been told that Charles II granted the baronetcy of Stichill - a village near Kelso - to Robert Pringle of Stichill, and the “male heirs from his body”, on January 5 1683.
The 10th Baronet, Sir Steuart Pringle, a retired Royal Marine commander who survived an IRA bomb attack, died in 2013 aged 84, judges have heard
Now his son Simon, and Murray - Simon’s second cousin - disagree over who should claim the title.
Lawyers for Murray Pringle say Simon should not become the 11th baronet because there has been a “break in the line of paternity”.
They say tests have shown that Sir Steuart’s DNA “did not match that of the Pringle lineage”.
James Guthrie QC, for Murray, suggested that the problem had arisen following the death of the 8th Baronet, Sir Norman Pringle, in 1919. He said Sir Norman and wife Florence had three sons: Norman, Ronald - Murray’s father - and James.
In 1920 Florence had made a formal “Statutory Declaration” saying Norman was the eldest son of the 8th baronet and was entitled to succeed to the title.
But Murray is arguing that the 8th baronet was not Norman’s father. And he claims that, as Ronald’s son, he is the rightful successor to the baronetcy.
Mr Guthrie said there had been “family gossip” and “tongues wagging” but he did not want to “make aspersions” against any baronet or any “ladies”.
Simon, whose legal team is headed by Timothy Scott QC, disputes Murray’s claim.