The appeal at the court in Sale, near Rabat, comes six weeks after three Islamic State group supporters were sentenced to death over the murders which have shocked the North African country.
The other defendants, including the only non-Moroccan, Spanish-Swiss Muslim convert Kevin Zoller Guervos, were handed jail terms ranging from five years to life.
While those convicted are seeking lighter punishments, the family of 24-year-old Danish student Louisa Vesterager Jespersen are urging the court to uphold the July 18th sentences, lawyers said.
Jespersen and her hiking companion 28-year-old Norwegian Maren Ueland, nature lovers who were training to be guides, were on a Christmas holiday hiking trip when they were killed.
The first hearing is expected to be taken up by procedural issues.
Prosecutors and social media users had called for the death penalty for all three main suspects, despite Morocco having a de facto freeze on executions since 1993.
Younes Ouaziyad, a 27-year-old carpenter who admitted to beheading one of the tourists, asked in court for "God's forgiveness".
Third alleged assailant, 33-year-old Rachid Afatti, had admitted to filming the brutal murders on his mobile phone.
Khaled El Fataoui, lawyer for Jespersen's family, aims to prove the state's moral responsibility for the killings and to seek financial compensation.
The court has ordered the three main accused to pay 2 million dirhams ($200,000) in compensation to Ueland's parents, although El Fataoui has said they did not have the means.
The defence team of those convicted has argued there were "mitigating circumstances on account of their precarious social conditions and psychological disequilibrium".
Coming from modest backgrounds, with a "very low" level of education, the defendants mostly lived in low-income areas of tourist hotspot Marrakesh.