Lawyers for the men have argued the letters were attempts to recruit the soldiers' families to a political view and were protected as political speech.

Man Haron Monis, also known as Sheikh Haron - a self-styled Muslim cleric - and his co-appellant, Amirah Droudis, sent letters to the widows and family members of several soldiers, referring to the dead men in what one judge described as ''a denigrating and derogatory fashion''.

Lawyers for Haron want the High Court to overturn indictments that he used the postal service to offend the families of fallen Diggers and relatives of a trade official killed by a bomb in Jakarta. The appeal will be determined on Wednesday.

with AAP