Logistics companies said the "Brexit" vote could have a two-pronged impact in the near term, potentially cutting into the movement of goods but also fueling more demand for services to help retailers and manufacturers navigate changing regulations and trade rules.

"There clearly is going to be a period of transition here where everyone is trying to figure out exactly how Brexit will take place. But it's not like the U.K. will stop trading with the EU and the U.S. or anyone else," said Andrew Clarke, chief financial officer at Minneapolis-based C.H. Robinson.

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