"We have cars from France, Denmark, Norway, Germany and a lot from Holland that are available for return journeys. But at the same time we are getting our Swedish registered cars back quicker from the continent," Anders Tärnell at Hertz Sweden told The Local on Monday.
Tärnell confirmed that the situation has created planning problems, with the firm's fleet unusually spread out across Europe and a build-up of cars arriving in Sweden.
"We have had parking problems - primarily in Gothenburg and Malmo. It is something of a logistical puzzle at the moment but we are coping," he said.
As air traffic problems on Friday began to render road routes to and from Sweden more attractive, car hire firms were quickly swamped with demand for their vehicles.
"We have been sold out since Friday but we are now starting to see a few cars available at stations across Sweden. We have closed our online booking system because of the high demand and encourage our customers to call their respective office," Lena Wikström at Europcar told The Local.
But the initial economic benefits could be short-lived with Anders Tärnell at Hertz arguing that everybody loses from continued flight problems in the longer term .
"We don't like this situation. We had high demand even before the problems started and so the initial upswing did not benefit us, and now fewer are travelling at all which means bookings are in fact down," he said, underlining that a return to normal would benefit all concerned.
This picture was confirmed by Staffan Wikström at Avis on Monday.
"Our regular rental prices are affected by demand, so prices were up slightly over the weekend, but if air traffic does not get going as normal we will all suffer in the longer term," he told The Local.
As the problems persisted on Monday, travellers were starting to change their habits, the firms confirmed.
"Many people are not not travelling at all. What we are seeing is fewer regular business bookings and more from those unable to get a flight and who are trying to get home," Anders Tärnell said.
"We are seeing a shift from airport locations to city locations. But in general I would say that the situation is under control," Staffan Wikström said.
"We are currently conducting an audit of our stocks to get a better overall picture of the situation," Lena Wikström said.
But despite the logistical problems, customers at Hertz and Avis can not count on any favourable prices for returning cars to their European homes.
"Normal prices apply. We have a one-way fee structure and this remains in place," Anders Tärnell confirmed.
"In certain cases we can negotiate, according to requirement, but in general we are holding to the same price structure for one-way rentals - it is the only fair way to deal with our customers," Staffan Wikström said.
But at Europcar, customers can expect some relief on one-way charges, while regular rental fees still apply.
"We have a larger number of foreign-registered cars, primarily in the bigger cities which have to be returned. While our normal rental charges apply we have cut some of our one-way fees to certain European destinations," Lena Wikström said.
"We are currently charging €200 ($270) for the one-way fee to Germany, the normal charge is €1,000," she confirmed.