His musical education began at the age of 3, his father, himself a musician, being the first teacher. The Central School of Music and Moscow Conservatory were the next steps. After the whole family emigrated and settled in New York in 1979, Nabatov continued his studies at the Juilliard School Of Music. By that time his interest and involvement in jazz and improvised music grew strong enough to make them his main activity.
Since then he performed and recorded with many fine musicians such as Paul Motian,Tony Scott, Sonny Fortune, Kenny Wheeler, Alan Skidmore, Herb Robertson, Louis Sclavis, Charles McPhearson, Billy Hart, David Murray, Paul Horn, Ricki Ford, Marty Ehrlich, Mark Dresser, Jim Snidero, Herb Geller, Dave Pike, Attila Zoller, Matthias Schubert, Barry Altschul, Vladimir Tarasov, John Betsch, Ed Schuller, Arto Tuncboyaci, Adam Nussbaum, Jay Clayton, Ron McClure, Mark Feldman, Drew Gress, Phil Minton, Michael Moore, Han Bennink, Misha Mengelberg, Wolter Wierbos and many others.