You can fly round trip from LAX to Moscow on Transaero Airlines for $741, including all taxes and fees but subject to availability, for travel between Oct. 1 and April 30. You must stay over a Saturday night.
Nonstop flights are available for travel Thursdays and Sundays in October and Sundays between November and March.
Info: Transaero Airlines, (877) 747-1191
Source: Airfarewatchdog