The case comes on top of an ongoing probe by Swiss prosecutors against Nazarbayev's son-in-law Timur Kulibayev for having allegedly laundered 600 million francs.
The first part of the latest lawsuit is once again targetted at Kulibayev.
It claims that when he was deputy chairman of the state-owned KazMunaiGaz, Kulibayev had purchased part of the company for $30 million before selling it on later for $340 million, said Bruno de Preux, the plaintiffs' lawyer, confirming a report in Matin Dimanche.
According to the newspaper, the profits from that transaction were banked at the Geneva branch of BNP Paribas on the account of a company called Oilex, which is controlled by one of Kulibayev's men.
The second part of the lawsuit concerns Nazarbayev, and claims that he pocketed $100 million in 2006 by appropriating the satellite television company Khabar Agency.
The transaction was completed through a member of Kazakhstan's mission to the UN in Geneva, who was also an appointee of Nazarbayev. Funds from this transaction have been deposited at Credit Suisse in Zurich, said the lawyer.
Swiss public prosecutors would neither confirm nor deny the case, but de Preux said that investigations were ongoing.