The appeal was filed by the group of former security officers and state officials convicted in the execution-style murder of opposition leader Altynbek Sarsenbaev and two aides.
Reports say at least six of the 10 defendants were attending the hearings, which are open to the press and international observers.
Naghiz Ak Zhol leader Sarsenbaev, a driver, and a bodyguard were found dead in the Almaty region in mid-February.
On August 31, a court in the city of Taldy-Qorgan sentenced former security officer Rustam Ibragimov to death over the killing, although Kazakhstan has had a moratorium on executions since 2003.
Nine others, including former Senate-administration official Yerzhan Utembaev, received prison terms of between three and 20 years.
Ibragimov and other defendants were reported to have confessed to participating in the killings, but all of them recanted in the courtroom and at least one implicated unnamed senior officials in the plot.
Sarsenbaev's relatives and fellow party members have accused officials of a coverup. They say those who were sentenced were mere executioners and that senior state officials commissioned the killing.
(Interfax-Kazakhstan, Kazakhstan Today)