New figures from the Central Statistics Office show that a total of 6,311 new private cars were licensed for the first time in September, up 6.5% on the same time last year.
The CSO also said that a total of 6,154 used, or imported, private cars were licensed, a big jump of 64.4% on the same month last year.
Today's figures show that in the first nine months of 2016, 136,044 new private cars were licensed, a rise of 18.9% compared with the same period last year.
And the number of used cars licensed increased by 34.9% compared with the same time in 2015.
There was also a 22.1% increase in the number of new goods vehicles licensed in September 2016 bringing the total to 2,053.
The CSO pointed out that licensing differs from registration in that a vehicle is licensed when a valid motor tax disc is issued for the first time. Registration occurs when a vehicle gets its registration number for the first time.
Figures released by SIMI earlier this week showed that new car registrations fell by 1.4% in September compared to the same month last year.
SIMI said that 162 registrations decreased by 1.4% to stand at a total of 4,698 compared to September 2015's figure of 4,766. Total new car registrations year to date are up 18% to 143,205, compared to 120,961 the same time last year.
Today's CSO figures also reveal that during the first nine months of 2016, 70% of new private cars licensed were diesel.
The figures also showed that Volkswagen was the most popular make of new car licensed in September with 845 VWs sold. This was followed by Ford with 610 sales, Toyota (507), Nissan (441) and Skoda (434).
The CSO said that these five makes represent 45% of all new private cars licensed.