A process for producing an .alpha.-olefin oligomer by oligomerization of
an .alpha.-olefin in a presence of a Ziegler-based catalyst, the process
comprising introducing at least a portion of a reaction product which is
taken out of a reactor and has a temperature of 115.degree. C. or higher
into an external heat exchanger, cooling the introduced reaction product,
maintaining an oligomerization solution taken out of the external heat
exchanger at a temperature of 110.degree. C. or higher and returning at
least a portion of the oligomerization solution to the reactor. In the
production of an .alpha.-olefin oligomer, precipitation and adhesion of
polymers at the inside of manufacturing apparatuses such as the external
heat exchanger and troubles caused thereby can be prevented and a stable
continuous operation can be continued for a long time.