There is disclosed a process for producing an .alpha.-olefin oligomer by
subjecting an .alpha.-olefin to oligomerization reaction in the presence
of a catalyst and an organic solvent which comprises the step of spraying
a solvent containing the organic solvent in the form of a linear or
bar-like pressure fluid toward a wall surface of a vapor phase portion of
a reactor from a nozzle fitted within a space of the vapor phase portion
of the reactor to conduct the oligomerization reaction while cleaning the
wall surface of the vapor phase portion of the reactor. In the production
process of the present invention, it is possible to effectively prevent
deposition of polymers onto the wall surface of the vapor phase portion
of the reactor and stably operate the reactor for a long period of time.