* Relative of Putin's former defence chief suspected of fraud
* Investigators say luxury cars rented out to defence ministry
* Latest case involving Serdyukov or someone close to him
By Steve Gutterman
MOSCOW, Jan 22 (Reuters) - Russian authorities said on Wednesday they are investigating former Defence Minister Anatoly Serdyukov's son-in-law on suspicion of fraud and embezzlement, adding to pressure on a one-time Kremlin insider fired by Vladimir Putin in 2012.
Serdyukov himself has been charged with negligence in one case and questioned in another, in legal action seen as both a test of Putin's stated determination to fight corruption and the result of Kremlin infighting.
The federal Investigative Committee said Serdyukov's son-in-law Valery Puzikov, the former deputy head of a Defence Ministry company, was being investigated on suspicion of involvement in a scheme involving luxury cars that the company rented out to the ministry.
The company paid commercial enterprises more than 8 million roubles ($235,800) between 2010 and 2013 for the use of high-end Mercedes, BMWs, Porches, Hummers and other vehicles that were not actually used by the ministry, the committee said.
The company also spent more that 4 million roubles on the salaries of employees who were hired for functions they did not carry out, such as one employed as a nurse, the committee said.
Puzikov could be sentenced to 10 years in prison if convicted of the charges, but Interfax news agency cited an unidentified source as saying authorities do not know where he is.
In power since 2000, Putin has repeatedly pledged to fight the corruption that has hampered post-Soviet Russia's development and discouraged investment, but critics say the problem has only worsened under his rule.
Opponents accuse the authorities of using allegations of corruption as a tool against rivals in business and politics.
Putin fired his longtime defence chief in November 2012 after a fraud scandal involving ministry property erupted involving a female subordinate of Serdyukov who was also his neighbour. Serdyukov has been treated only as a witness in that case.
However, in December he was charged with negligence in a separate case in which he is accused of ordering troops to build a road to a luxury resort, and faces up to three months in jail or a year of "corrective work" or community service. ($1 = 33.9337 Russian roubles) (Editing by Sonya Hepinstall)