Space Adventures will launch its first circumlunar mission in 2018, according to the Russian news service Interfax. Political factors could disrupt the trip, however.
The mission would use a modified Soyuz capsule, which would rendezvous and dock with a Russian upper stage. The upper stage would then be used to propel the Soyuz onto a circumlunar trajectory, in a manner similar to what was once planned for Lunar Gemini flights.
Before heading to the Moon, the Soyuz crew (Russian cosmonaut pilot and two Space Adventures customers) would spend about 10 days at the International Space Station. This would allow the crew to adapt to the weightless environment, so any problems with space sickness would be past before the circumlunar leg begins.
Space Adventures has been marketing the lunar flight for several years now. Filling the first seat was apparently no problem, but selling the second seat caused some delay. In June 2014, Space Adventures announced that it had sold the second seat and the project was ready to begin. (Seats reportedly sell for $150 million.)
Reaction from Russia has been mixed, however. The Russian space company Energia expressed some enthusiasm for the project. A few weeks later, the Russian Space Agency (RSA or Roscosmos) repudiated the plan.
It’s possible that Space Adventures and Energia could carry out the mission without participation from the Russian Space Agency, but the Russian government has recently been asserting increased control over the Russian space industry. The government currently owns 38% of Energia stock but is seeking majority control. In August, Energia president Vitaly Lopota was suspended from his post. Lapota has been under criminal investigation for abuse of office, a charge that is widely seen as politically motivated.
The Russian government has announced ambitious space plans which include lunar missions, but Russia has the habit of announcing grandiose plans which are never funded. Even if lunar missions do occur, it remains to be seen if Russia has any interest in cooperating with US commercial space companies.