Tyrmyev was sentenced to 10 years in jail in 2002 after being convicted of abuse of power.
Family members tell RFE/RL's Turkmen Service that earlier this year, 10 days before Tyrmyev's sentence was due to end, a new criminal case was opened against him, reportedly in connection with a fight with another inmate.
They say Tyrmyev, believed to be in his late 50s, was sentenced to seven more years in jail at a closed-door hearing on March 6.
Members of Tyrmyev's family, who live in Dashoguz Province, say they have not been allowed to see him or communicate with him since the summer of 2002. The exact location of his imprisonment is not known.
"We don’t know anything about [his health]," a close relative who did not wish to be identified told RFE/RL. "That’s why we are asking the authorities to allow us to send him [basic necessities]. We are asking them to create an option for us where we can communicate with him and send and receive letters.”