The latest Your Move/Acadata Scottish House Price Index states two thirds of local authorities experienced growth for the second month in a row.
Overall, 21 out of 32 regions saw prices rise, led by Inverclyde (up 5.7%), Clackmannanshire (5%) and South Ayrshire and North Ayrshire (which both saw prices up 4.4%).
Glasgow also set a new peak price, with average prices rising 0.8% to £147,974. Average prices are now exactly £9,000 more (+6.5%) than during the same period last year.
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Latest ONS transactions figures have also increased, up 7% in May over April but down 17% on the same month last year. Your Move stated this is due to large numbers of property purchases brought forward to March ahead of April's introduction of an additional 3% Land and Buildings Transaction Tax (LBTT) surcharge on second homes.
Christine Campbell, Managing Director of Your Move in Scotland, said Glasgow's progress is a sign the Scottish housing market is proving "remarkably resilient".
"While tax changes have seen a slowdown in transactions of high priced property in Scotland, the market overall is demonstrating broad-based growth. So far this growth seems to be holding steady in an uncertain future post-Brexit."
(LM/MH)
