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.

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> Method of optimizing the operation of a xylene separation unit using simulated countercurrent

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